Reception device

ABSTRACT

It is possible to demodulate a plurality of modulated signals transmitted from a plurality of antennas by using a comparatively small-size circuit with a preferable error ratio characteristic. Partial bit judgment units ( 509, 512 ) demodulates partial bits of the 64 QAM-modulated signal by modifying which of the bits in the 6-bit strings constituting a symbol is to be demodulated depending on in which region of the IQ plane the reception signal point exists. This improves the partial bit error characteristic judged by the partial bit judgment units ( 509, 512 ), which in turn improves reliability of the reduced candidate signal point for use by a likelihood detection unit ( 518 ). As a result, it is possible to improve the error ratio characteristic of the final reception digital signals ( 322, 323 ).

TECHNICAL FIELD

The present invention relates to a receiving apparatus that receives and demodulates modulated signals transmitted simultaneously from a plurality of antennas and a transmitting apparatus that transmits modulated signals simultaneously from a plurality of antennas.

BACKGROUND ART

Hitherto, the technology disclosed in Non-Patent Document 1 has been known as a demodulation method using a plurality of antennas. The contents disclosed in this Non-Patent Document 1 are briefly described below using an accompanying drawing.

In FIG. 1, in a transmitting apparatus 30, a transmit signal A digital signal 1 and transmit signal B digital signal 2 are input to a modulated signal generation section 3. Modulated signal generation section 3 executes BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), 16QAM (Quadrature Amplitude Modulation), or suchlike modulation on transmit signal A digital signal 1 and transmit signal B digital signal 2, thereby obtaining a transmit signal A baseband signal 4 and transmit signal B baseband signal 5, and sends these signals to a radio section 6.

Radio section 6 executes predetermined radio processing such as frequency conversion and amplification on transmit signal A baseband signal 4 and transmit signal B baseband signal 5, thereby obtaining a transmit signal A modulated signal 7 and transmit signal B modulated signal 8, and supplies these signals to an antenna 9 and antenna 10 respectively. By this means, transmit signal A modulated signal 7 is emitted as a radio wave from antenna 9, and transmit signal B modulated signal 8 is emitted as a radio wave from antenna 10.

In a receiving apparatus 40, a radio section 13 executes radio processing such as frequency conversion and amplification on a received signal 12 received by an antenna 11, thereby obtaining a baseband signal 14, and sends this signal to a maximum likelihood detection section 19. Similarly, a radio section 17 executes radio processing such as frequency conversion and amplification on a received signal 16 received by an antenna 15, thereby obtaining a baseband signal 18, and sends this signal to maximum likelihood detection section 19.

By detecting baseband signals 14 and 18, maximum likelihood detection section 19 obtains a transmit signal A received digital signal 20 and transmit signal B received digital signal 21 at this time, maximum likelihood detection section 19 performs Maximum Likelihood Detection (MLD) as shown in Non-Patent Document 1.

Non-patent Document 1: IEEE WCNC 1999, pp. 1038-1042, September 1999.

DISCLOSURE OF INVENTION Problems to be Solved by the Invention

However, with the configuration in FIG. 1, if 16QAM is performed by modulated signal generation section 3, for example, when MLD is performed by maximum likelihood detection section 19, it is necessary to find the Euclidian distances between 16×16=256 candidate signal points and a received signal. Furthermore, if 64QAM is performed by modulated signal generation section 3, when MLD is performed by maximum likelihood detection section 19, it is necessary to find the Euclidian distances between 64×64=4096 candidate signal points and a received signal. When detection is performed by means of such computations, while good reception quality (bit error rate performances) can certainly be achieved, there is a problem in that the computational complexity is large because of the large number of computations. As described above, this problem becomes more pronounced as the modulation M-ary number increases.

It is an object of the present invention to provide a receiving apparatus that can demodulate a plurality of modulated signals transmitted from a plurality of antennas with a comparatively small computational complexity and good bit error rate performances. It is also an object of the present invention to provide a transmitting apparatus that forms a transmit signal such that a received signal with good bit error rate performances can be obtained on the receiving side with a comparatively small computational complexity.

MEANS FOR SOLVING THE PROBLEMS

A receiving apparatus of the present invention for solving these problems receives modulated signals transmitted from a transmitting apparatus that transmits different modulated signals from a plurality of antennas; and employs a configuration that includes: a channel fluctuation estimation section that finds a channel estimate of each modulated signal; a partial bit demodulation section that demodulates only some bits of a modulated signal using a detection method different from likelihood detection; a signal point reduction section that reduces the number of candidate signal points using demodulated partial bits and a channel estimate; and a likelihood detection section that performs likelihood detection using a reduced number of candidate signal points and a received baseband signal.

According to this configuration, since demodulation of only some bits is performed by the partial bit demodulation section using a detection method different from likelihood detection, partial bits can be obtained with a small amount of computation. Also, likelihood detection is performed by the likelihood detection section using a reduced number of candidate signal points so that the remaining bits can be found with a high degree of precision using a small amount of computation. As likelihood detection is performed on a partial basis in this way, a received digital signal with good bit error rate performances can be obtained while reducing the number of computations for finding Euclidian distances.

A receiving apparatus of the present invention employs a configuration wherein the partial bit demodulation section, in demodulating some bits of a modulated signal that has undergone 64QAM modulation, changes which bit in a 6-bit bit string making up one symbol is demodulated as a partial bit according to which area on the IQ plane the relevant reception signal point is present in.

According to this configuration, the bit error performance of a partial bit demodulated by the partial bit demodulation section improves, and therefore the reliability of reduced candidate signal points used by the likelihood detection section improves. As a result, the bit error performance of final demodulated bits can be improved.

ADVANTAGEOUS EFFECT OF THE INVENTION

According to the present invention, a receiving apparatus can be realized that can demodulate a plurality of modulated signals transmitted from a plurality of antennas with a comparatively small computational complexity and good bit error rate performances. Also, a transmitting apparatus can be realized that forms a transmit signal such that a received signal with good bit error rate performances can be obtained on the receiving side with a comparatively small computational complexity.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram showing a schematic configuration of a conventional multi-antenna transmitting apparatus and receiving apparatus;

FIG. 2 is a block diagram showing the configuration of a transmitting apparatus according to Embodiment 1 of the present invention;

FIG. 3 is a drawing showing frame configurations of Embodiment 1;

FIG. 4 is a block diagram showing the configuration of a receiving apparatus according to Embodiment 1 of the present invention;

FIG. 5 is a block diagram showing the configuration of a signal processing section of a receiving apparatus;

FIG. 6 is a drawing showing the relationship of transmitting and receiving antennas in Embodiment 1;

FIG. 7A is a drawing showing a 16QAM bit arrangement applied to modulated signal A;

FIG. 7B is a drawing showing a 16QAM bit arrangement applied to modulated signal B;

FIG. 8 is a drawing showing a sample signal point arrangement of estimated signal points (candidate signal points) when a 16 QAM modulated signal A and 16 QAM modulated signal B are received;

FIG. 9A is a drawing showing a 16QAM bit arrangement;

FIG. 9B is a drawing showing an area division method for 16QAM partial bit determination according to Embodiment 1;

FIG. 10 is a drawing showing the signal point state after signal point reduction according to Embodiment 1;

FIG. 11A is a drawing showing a 16QAM bit arrangement;

FIG. 11B is a drawing showing an area division method for partial bit determination of two 16QAM bits;

FIG. 12 is a block diagram showing the configuration of a transmitting apparatus of Embodiment 1;

FIG. 13A is a drawing showing the frame configuration of modulated signal A transmitted from the transmitting apparatus in FIG. 12;

FIG. 13B is a drawing showing the frame configuration of modulated signal B transmitted from the transmitting apparatus in FIG. 12;

FIG. 14 is a block diagram showing the configuration of a receiving apparatus that receives a signal from the transmitting apparatus in FIG. 12;

FIG. 15A is a drawing showing a signal point arrangement by a transmitting apparatus of Embodiment 2;

FIG. 15B is a drawing showing an area division method at the time of partial bit determination by a receiving apparatus of Embodiment 2;

FIG. 16 is a block diagram showing another sample configuration of a signal processing section of Embodiment 2;

FIG. 17 is a drawing showing a 64QAM signal point arrangement;

FIG. 18 is a drawing showing a signal point arrangement by a transmitting apparatus of Embodiment 3 and an area division method for partial bit determination by a receiving apparatus;

FIG. 19 is a drawing showing a signal point arrangement by a transmitting apparatus of Embodiment 3 and an area division method for partial bit determination by a receiving apparatus;

FIG. 20 is a block diagram showing the configuration of a transmitting apparatus of Embodiment 4;

FIG. 21 is a block diagram showing a configuration of a signal processing section of a receiving apparatus of Embodiment 4;

FIG. 22 is a drawing provided to explain computational processing by the soft decision value calculation section in FIG. 21;

FIG. 23 is a block diagram showing another sample configuration of a signal processing section of Embodiment 4;

FIG. 24 is a block diagram showing a configuration of a coding section of Embodiment 5;

FIG. 25A is a drawing showing the configuration of a partial bit determination section that determines partial bits of modulated signal A according to Embodiment 5;

FIG. 25B is a drawing showing the configuration of a partial bit determination section that determines partial bits of modulated signal B according to Embodiment 5;

FIG. 25C is a drawing showing the configuration of a likelihood detection section of Embodiment 5;

FIG. 26 is a block diagram showing another sample configuration of a coding section of Embodiment 5;

FIG. 27 is a block diagram showing another sample configuration of a signal processing section of a receiving apparatus according to Embodiment 5;

FIG. 28 is a block diagram showing the configuration of a modulation section for performing trellis coding modulation according to Embodiment 6;

FIG. 29 is a drawing showing an area division method for partial bit determination of a BPSK signal;

FIG. 30 is a block diagram showing the configuration of a transmitting apparatus of Embodiment 7;

FIG. 31 is a drawing showing frame configurations of Embodiment 7;

FIG. 32 is a block diagram showing the configuration of a receiving apparatus of Embodiment 7;

FIG. 33 is a block diagram showing a configuration of a signal processing section of a receiving apparatus according to Embodiment 7;

FIG. 34 is a block diagram showing another configuration of a signal processing section of a receiving apparatus according to Embodiment 7;

FIG. 35 is a drawing provided to explain 1-bit determination processing of Embodiment 8;

FIG. 36 is a flowchart showing the 1-bit determination processing procedure of Embodiment 8;

FIG. 37 is a drawing provided to explain area division of Embodiment 9;

FIG. 38 is a drawing provided to explain area division of Embodiment 9;

FIG. 39 is a drawing provided to explain Manhattan distance and Euclidian distance according to Embodiment 11;

FIG. 40 is a drawing provided to explain approximation of Euclidian distances using Manhattan distances according to Embodiment 11;

FIG. 41 is a block diagram showing a sample circuit configuration for likelihood detection of Embodiment 11;

FIG. 42 is a flowchart showing the partial bit determination processing procedure of Embodiment 12;

FIG. 43 is a block diagram showing the configuration of a signal processing section of a receiving apparatus according to Embodiment 13;

FIG. 44 is a block diagram showing the configuration of a signal processing section of a receiving apparatus according to Embodiment 14; and

FIG. 45 is a block diagram showing the configuration of a signal processing section of a receiving apparatus according to Embodiment 15.

MODES FOR CARRYING OUT THE INVENTION

Embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

Embodiment 1

FIG. 2 shows the configuration of a transmitting apparatus of this embodiment. In transmitting apparatus 100, digital signal 101 is input to modulation section 102, and digital signal 109 is input to modulation section 110.

Modulation section 102 has digital signal 101 and frame configuration signal 118 as input, modulates digital signal 101 in accordance with frame configuration signal 118, and sends baseband signal 103 thus obtained to spreading section 104. Spreading section 104 multiplies baseband signal 103 by a spreading code, and sends a spread baseband signal 105 thus obtained to radio section 106. Radio section 106 executes frequency conversion, amplification, and so forth on spread baseband signal 105, thereby obtaining modulated signal 107. Modulated signal 107 is output as a radio wave from an antenna 108.

Modulation section 110 has digital signal 109 and frame configuration signal 118 as input, modulates digital signal 109 in accordance with frame configuration signal 118, and sends baseband signal 111 thus obtained to spreading section 112. Spreading section 112 multiplies baseband signal 111 by a spreading code, and sends spread baseband signal 113 thus obtained to radio section 114. Radio section 114 executes frequency conversion, amplification, and so forth on spread baseband signal 113, thereby obtaining modulated signal 115. Modulated signal 115 is output as a radio wave from an antenna 116.

In the following description, a signal transmitted from antenna 108 is referred to as modulated signal A, and a signal transmitted from antenna 116 is referred to as modulated signal B.

Frame configuration signal generation section 117 outputs information indicating frame configurations—such as information on the frame configurations in FIG. 3, for example—as frame configuration signal 118.

FIG. 3 shows sample frame configurations of modulated signals transmitted from antennas 108 and 116 of transmitting apparatus 100. Modulated signal A transmitted from antenna 108 and modulated signal B transmitted from antenna 116 have channel estimation symbols 201 and 203 for channel estimation, and data symbols 202 and 204. Transmitting apparatus 100 transmits modulated signal A and modulated signal B with the frame configurations shown in FIG. 3 at virtually the same time. Channel estimation symbols 201 and 203 for channel estimation can also be referred to as pilot symbols, unique words, or preambles.

FIG. 4 shows the configuration of a receiving apparatus of this embodiment. Receiving apparatus 300 receives signals from two antennas 301 and 311.

A radio section 303 has received signal 302 received by antenna 301 as input, executes frequency conversion, quadrature demodulation, and so forth on received signal 302, and sends baseband signal 304 thus obtained to despreading section 305. Despreading section 305 despreads baseband signal 304, and outputs despread baseband signal 306 thus obtained.

Modulated signal A channel fluctuation estimation section 307 has despread baseband signal 306 as input, estimates channel fluctuation using modulated signal A channel estimation symbol 201 in the frame configuration in FIG. 3, for example, and sends modulated signal A channel fluctuation signal 308 thus obtained to signal processing section 321. Similarly, modulated signal B channel fluctuation estimation section 309 has despread baseband signal 306 as input, estimates channel fluctuation using modulated signal B channel estimation symbol 203 in the frame configuration in FIG. 3, for example, and sends modulated signal B channel fluctuation signal 310 thus obtained to signal processing section 321.

Radio section 313 has received signal 312 received by antenna 311 as input, executes frequency conversion, quadrature demodulation, and so forth on received signal 312, and sends baseband signal 314 thus obtained to despreading section 315. Despreading section 315 despreads baseband signal 314, and outputs despread baseband signal 316 thus obtained.

Modulated signal A channel fluctuation estimation section 317 has despread baseband signal 316 as input, estimates channel fluctuation using modulated signal A channel estimation symbol 201 in the frame configuration in FIG. 3, for example, and sends modulated signal A channel fluctuation signal 318 thus obtained to signal processing section 321. Similarly, modulated signal B channel fluctuation estimation section 319 has despread baseband signal 316 as input, estimates channel fluctuation using modulated signal B channel estimation symbol 203 in the frame configuration in FIG. 3, for example, and sends modulated signal B channel fluctuation signal 320 thus obtained to signal processing section 321.

Signal processing section 321 has despread baseband signals 306 and 316, modulated signal A channel fluctuation signals 308 and 318, and modulated signal B channel fluctuation signals 310 and 320 as input, and by performing modulated signal A and B detection, decoding, and so forth, using these signals, obtains modulated signal A digital signal 322 and modulated signal B digital signal 323. The detailed configuration of signal processing section 321 is shown in FIG. 5, and details of its operation will be described later herein.

FIG. 6 shows the relationship between transmitting and receiving apparatuses according to this embodiment. Assume that a signal transmitted from antenna 108 of transmitting apparatus 100 is designated Txa(t), and a signal transmitted from antenna 116, Txb(t); a signal received by antenna 301 of receiving apparatus 300 is designated Rx1(t), and a signal received by antenna 311, Rx2(t); and propagation fluctuations between the antennas are designated h11(t), h12(t), h21(t), and h22(t). Then the relational expression in the following equation holds true, where t denotes time.

$\begin{matrix} {\begin{pmatrix} {{Rx}\; 1(t)} \\ {{Rx}\; 2(t)} \end{pmatrix} = {\begin{pmatrix} {h\; 11(t)} & {h\; 21(t)} \\ {h\; 12(t)} & {h\; 22(t)} \end{pmatrix}\begin{pmatrix} {{Txa}(t)} \\ {{Txb}(t)} \end{pmatrix}}} & (1) \end{matrix}$

FIG. 7A and FIG. 7B show the signal point arrangements and bit assignments of modulated signal A and modulated signal B when 16QAM (Quadrature Amplitude Modulation) is performed by modulation sections 102 and 110. FIG. 7A shows the signal point arrangement and bit assignments of modulated signal A, and FIG. 7B shows the signal point arrangement and bit assignments of modulated signal B. For both modulated signal A and modulated signal B, 4 bits are assigned to one symbol. In this embodiment, for the sake of explanation, the 4 bits assigned to one symbol of modulated signal A are designated (Sa0, Sa1, Sa2, Sa3), and the 4 bits assigned to one symbol of modulated signal B are designated (Sb0, Sb1, Sb2, Sb3). That is to say, (Sa0, Sa1, Sa2, Sa3) and (Sb0, Sb1, Sb2, Sb3) can each have 16 values from (0, 0, 0, 0) to (1, 1, 1, 1).

When modulated signal A and modulated signal B are 16QAM signals as shown in FIG. 7A and FIG. 7B, there are 16×16=256 signal points in a multiplexed received signal. Estimated signal points for these 256 signal points in the I-Q plane can be obtained from modulated signal A channel fluctuation signal 308 and modulated signal B channel fluctuation signal 310 in FIG. 4. An example of this signal point arrangement is shown in FIG. 8. Black dots in FIG. 8 indicate 256 estimated signal points. Reference code 701 indicates a signal point of despread baseband signal 306 in FIG. 4. At this time, modulated signal A and modulated signal B decoding and detection can be performed by finding the signal point distances between the 256 estimated signal points and despread-baseband-signal signal point 701, and seeking the estimated signal point with the smallest distance value. For example, reference code 702 indicates an estimated signal point for which (Sa0, Sa1, Sa2, Sa3, Sb0, Sb1, Sb2, Sb3) is (0, 0, 0, 0, 0, 0, 0, 0), and in the case shown in FIG. 8, reception point 701 is at the smallest distance from estimated signal point 702 among the 256 estimated signal points, enabling (0, 0, 0, 0, 0, 0, 0, 0) to be obtained as the detection result.

A drawback with performing detection in this way is that it is necessary to find the signal point distances between a reception point and all 256 estimated signal points, and therefore the computational complexity is extremely large. However, an advantage is that good reception quality (data with good bit error rate performances) can be obtained. On the other hand, a detection method in which the inverse matrix computation of the relational expression of Equation (1) is performed enables the computational complexity to be reduced, but has a drawback of poor bit error rate performances.

Receiving apparatus 300 of this embodiment is configured based on the features of both these methods, enabling receive data of high quality (with good bit error rate performances) to be obtained with a small computational complexity.

FIG. 5 shows the detailed configuration of signal processing section 321, which is a feature of receiving apparatus 300 of this embodiment.

A separation section 507 has modulated signal A channel fluctuation signals 308 and 318, modulated signal B channel fluctuation signals 310 and 320, and despread baseband signals 306 and 316 as input, and obtains estimated signals of transmit signals Txa(t) and Txb(t) by performing the inverse matrix computation of Equation (1). Separation section 507 sends thus obtained modulated signal A estimated baseband signal 508 to partial bit determination section 509, and also sends modulated signal B estimated baseband signal 511 to partial bit determination section 512.

Here, separation section 507 and partial bit determination sections 509 and 512 make up partial bit demodulation section 550 that demodulates only some bits of modulated signals A and B using a detection method different from likelihood detection. In this embodiment, a case is described in which Equation (1) inverse matrix computation is performed by separation section 507, but a received signal in which a plurality of modulated signals are mixed together may also be separated into modulated signals A and B by performing MMSE computation, for example, the essential point being that only some bits of modulated signals A and B are demodulated using a detection method different from likelihood detection.

The operation of partial bit determination sections 509 and 512 will now be explained. Partial bit determination section 509 and partial bit determination section 512 perform similar operations, with only the signals processed being different, and therefore the operation of partial bit determination section 509 for modulated signal A will be described here. FIG. 9A shows the arrangement of the coordinates of the 16 signal points (symbols) of 16QAM. As can be seen, the 4 bits (Sa0, Sa1, Sa2, Sa3) making up one modulated signal A symbol can have a value from (0, 0, 0, 0) to (1, 1, 1, 1) according to the signal point location.

Partial bit determination section 509 has modulated signal A estimated baseband signal 508 as input, determines Sa0=1 when modulated signal A estimated baseband signal 508 is present in area 1 shown in FIG. 9B, Sa0=0 when present in area 2, Sa2=1 when present in area 3, Sa2=0 when present in area 4, and Sa3=1 when present in area 5, and outputs this information as modulated signal A determined partial bit information 510. Partial bit determination section 512 has modulated signal B estimated baseband signal 511 as input, performs the same kind of operation as described above, and outputs modulated signal B determined partial bit information 513.

The reason for setting the areas that determine 1 bit as shown in FIG. 9B is that 1 bit set as shown in FIG. 9B from among Sa0, Sb1, Sa2, and Sa3 has a higher probability of being correct than the remaining 3 bits. Therefore, if this 1 bit is determined, there is a low probability of degradation of reception quality in subsequent detection.

Next, the operation of signal point reduction sections 514 and 516 will be explained. Signal point reduction section 514 has modulated signal A channel fluctuation estimation signal 318, modulated signal B channel fluctuation estimation signal 320, modulated signal A determined partial bit information 510, and modulated signal B determined partial bit information 513 as input. If signal point reduction were not performed here, 256 signal point candidate points would be found from modulated signal A channel fluctuation estimation signal 318 and modulated signal B channel fluctuation estimation signal 320 as shown in FIG. 8. However, in this embodiment, by using modulated signal A determined partial bit information 510 and modulated signal B determined partial bit information 513, as described above, from bit-by-bit determination information (a total of 2 bits), only 8−2=6 bits (64 signal points) are undetermined of the 8 bits (256 signal points). For example, assume that Sa0=1 information is input to signal point reduction section 514 as modulated signal A determined partial bit information 510, and Sb0=0 information is input to signal point reduction section 514 as modulated signal B determined partial bit information 513. Signal point reduction section 514 then eliminates signal points that do not have Sa0=1 and Sb0=0 values from among the 256 signal points (FIG. 8). By this means, the number of candidate signal points can be reduced to 64, and signal point reduction section 514 outputs information of these 64 signal points as post-reduction signal point information 515. Signal point reduction section 516 has modulated signal A channel fluctuation signal 308, modulated signal B channel fluctuation signal 310, modulated signal A determined partial bit information 510, and modulated signal B determined partial bit information 513 as input, performs the same kind of operation as described above, and outputs post-reduction signal point information 517.

A likelihood detection section 518 has despread baseband signals 306 and 316, and post-reduction signal point information 515 and 517, as input. Then the state in FIG. 10 is obtained from post-reduction signal point information 515 and despread baseband signal 316. In FIG. 10, despread baseband signal 316 is the signal point indicated by reference code 701, and post-reduction signal point information 515 comprises the 64 signal points indicated by black dots. Likelihood detection section 518 then finds the signal point distances between the 64 candidate signal points and despread-baseband-signal signal point 701. That is to say, likelihood detection section 518 finds a branch metric. This is named branch metric X. Similarly, likelihood detection section 518 finds the signal point distances between the 64 candidate signal points and despread-baseband-signal signal point 701 from post-reduction signal point information 517 and despread baseband signal 306. That is to say, likelihood detection section 518 finds a branch metric. This is named branch metric Y.

Then likelihood detection section 518 finds the 8-bit sequence with the highest likelihood using branch metric X and branch metric Y, and outputs this as modulated signal A digital signal 322 and modulated signal B digital signal 323. In the example in FIG. 5, likelihood detection section 518 separates and outputs (in parallel) modulated signal A and modulated signal B digital signals 322 and 323, but modulated signal A and modulated signal B digital signals may also be bundled and output (in series) as a single digital signal.

Thus, according to this embodiment, by providing partial bit demodulation section 550 that determines partial bits from among a plurality of bits that make up one symbol of each modulated signal using a detection method different from likelihood detection, signal point reduction sections 514 and 516 that reduce the number of candidate signal points using the determined partial bits, and likelihood detection section 518 that obtains received digital signals 322 and 323 by performing likelihood detection based on the Euclidian distances between reduced candidate signal points and a reception point, a receiving apparatus 300 can be realized that enables bit error rate performances to be effectively improved with a comparatively small computational complexity. That is to say, as a reduced number of candidate signal points are used by likelihood detection section 518, the number of computations for finding Euclidian distances is reduced, enabling the computational complexity to be decreased. Also, as partial bits found based on inverse matrix computation results are only bits unlikely to be erroneous, degradation of bit error rate performances due to inverse matrix computation can be greatly suppressed compared with a case in which likelihood decoding of all bits is performed based on inverse matrix computation results.

(i) Another Sample Configuration of a Partial Bit Determination Section

In the above embodiment, a case has been described in which a reduction in the number of candidate signal points of a total of 2 bits is performed by signal point reduction sections 514 and 516 respectively by having bit determination performed one bit at a time by partial bit determination sections 509 and 512. Here, a method and configuration will be described whereby a reduction in the number of candidate signal points of a total of 4 bits is performed by signal point reduction sections 514 and 516 respectively by having bit determination performed 2 bits at a time by partial bit determination sections 509 and 512.

FIG. 11A and FIG. 11B show an example of a determination method for determining 2 bits by partial bit determination sections 509 and 512 in FIG. 8. Partial bit determination section 509 and partial bit determination section 512 perform similar operations, with only the signals processed being different, and therefore the operation of partial bit determination section 509 for modulated signal A will be described here. FIG. 11A shows the arrangement of the coordinates of the 16 signal points (symbols) of 16QAM. As can be seen, the 4 bits (Sa0, Sa1, Sa2, Sa3) making up one modulated signal A symbol can have any value from (0, 0, 0, 0) to (1, 1, 1, 1) according to the signal point location.

Partial bit determination section 509 has modulated signal A estimated baseband signal 508 as input, determines Sa0=0 and Sa2=1 when modulated signal A estimated baseband signal 508 is present in area 1 bounded by dotted lines in FIG. 11B, Sa1=1 and Sa2=1 when present in area 2, Sa0=1 and Sa2=1 when present in area 3, Sa0=0 and Sa3=1 when present in area 4, Sa1=1 and Sa3=1 when present in area 5, Sa0=1 and Sa3=1 when present in area 6, Sa0=0 and Sa2=0 when present in area 7, Sa1=1 and Sa2=0 when present in area 8, and Sa0=1 and Sa2=0 when present in area 9. Partial bit determination section 509 then outputs this information as modulated signal A determined partial bit information 510. Partial bit determination section 512 has modulated signal B estimated baseband signal 511 as input, performs the same kind of operation as described above, and outputs modulated signal B determined partial bit information 513.

The reason for setting the areas that determine 2 bits as shown in FIG. 11B is that 2 bits set as shown in FIG. 11B from among Sa0, Sb1, Sa2, and Sa3 have a higher probability of being correct than the remaining 2 bits. Therefore, if these 2 bits are determined, there is a low probability of degradation of reception quality in subsequent detection.

Signal point reduction section 514 performs candidate signal point reduction by carrying out the same kind of operations as described above. At this time, since modulated signal B determined partial bit information 513 is composed of 2 bits, only 8−4=4 bits (16 signal points) are undetermined of the 8 bits (256 signal points). By this means, the number of candidate signal points can be reduced to 16. Information of these 16 signal points forms post-reduction signal point information. Therefore, branch metric calculation can be further reduced in likelihood detection section 518, and the computational complexity can be further decreased However, as the number of bits determined by partial bit determination sections 509 and 512 increases, reception quality degrades.

(ii) Application to a Multicarrier System

A sample configuration will be described here for a case in which the present invention is applied to a multicarrier system. A case in which OFDM (Orthogonal Frequency Division Multiplexing) scheme is used as a multicarrier system will be described as an example.

FIG. 12 shows the configuration of a transmitting apparatus. In transmitting apparatus 1100, a digital signal 1101 is input to a modulation section 1102, and a digital signal 1111 is input to a modulation section 1112.

Modulation sections 1102 and 1112 have digital signals 1101 and 1111, and a frame configuration signal 1122, as input, modulate digital signals 1101 and 1111 in accordance with frame configuration signal 1122, and send baseband signals 1103 and 1113 thus obtained to serial/parallel conversion sections (S/Ps) 1104 and 1114. Serial/parallel conversion sections 1104 and 1114 perform serial/parallel conversion of baseband signals 1103 and 1113 respectively, and send parallel signals 1105 and 1115 thus obtained to inverse Fourier transform sections (idft's) 1106 and 1116 respectively. Inverse Fourier transform sections 1106 and 1116 execute inverse Fourier transform processing on parallel signals 1105 and 1115 respectively, and send post-inverse-Fourier-transform signals 1107 and 1117 thus obtained to radio sections 1108 and 1118 respectively. Radio sections 1108 and 1118 execute frequency conversion, signal amplification, and so forth on post-inverse-Fourier-transform signals 1107 and 1117 respectively, thereby obtaining modulated signals 1109 and 1119. Modulated signals 1109 and 1119 are output as radio waves from antennas 1110 and 1120 respectively.

By this means, modulated signal 1109 (modulated signal A) and modulated signal 1119 (modulated signal B), which are OFDM signals, are transmitted from antennas 1110 and 1120 respectively.

Here, a frame configuration signal generation section 1121 outputs frame configuration information as frame configuration signal 1122. Sample frame configurations are shown in FIG. 13A and FIG. 13B. In FIG. 13A and FIG. 13B, frame configurations are represented on time-frequency axes. FIG. 13A shows a frame configuration of modulated signal A, and FIG. 13B shows a frame configuration of modulated signal B. As an example, a case is shown in which a frame is composed of carrier 1 through carrier 5. It is assumed that symbols of the same time slot are transmitted at the same time. Pilot symbols 1201 indicated by hatching are symbols for performing channel estimation on the receiving side. Although these symbols are referred to here as pilot symbols, they may also be given another designation such as “preamble,” and need only be symbols that enable channel estimation to be performed. Blanks indicated by reference code 1202 denote data symbols.

FIG. 14 shows the configuration of a receiving apparatus. Receiving apparatus 300 receives signals by means of two antennas 1301 and 1311.

A radio section 1303 has a received signal 1302 received by antenna 1301 as input, executes frequency conversion and so forth on received signal 1302, and sends a baseband signal 1304 thus obtained to a Fourier transform section (dft) 1305. Fourier transform section 1305 performs Fourier transform processing on baseband signal 1304, and outputs a post-Fourier-transform signal 1306 thus obtained.

A modulated signal A channel fluctuation estimation section 1307 has post-Fourier-transform signal 1306 as input, finds modulated signal A channel fluctuation for carrier 1 through carrier 5 using modulated signal A pilot symbols 1201 in FIG. 13A, and outputs a modulated signal A channel fluctuation signal group 1308 (composed of estimation signals for carrier 1 through carrier 5). Similarly, a modulated signal B channel fluctuation estimation section 1309 has post-Fourier-transform signal 1306 as input, finds modulated signal B channel fluctuation for carrier 1 through carrier 5 using modulated signal B pilot symbols 1201 in FIG. 13B, and outputs a modulated signal B channel fluctuation signal group 1310 (composed of estimation signals for carrier 1 through carrier 5).

Similarly, a radio section 1313 has a received signal 1312 received by antenna 1311 as input, executes frequency conversion and so forth on received signal 1312, and sends a baseband signal 1314 thus obtained to a Fourier transform section (dft) 1315. Fourier transform section 1315 performs Fourier transform processing on baseband signal 1314, and outputs a post-Fourier-transform signal 1316 thus obtained.

A modulated signal A channel fluctuation estimation section 1317 has post-Fourier-transform signal 1316 as input, finds modulated signal A channel fluctuation for carrier 1 through carrier 5 using modulated signal A pilot symbols 1201 in FIG. 13A, and outputs a modulated signal A channel fluctuation signal group 1318 (composed of estimation signals for carrier 1 through carrier 5). Similarly, a modulated signal B channel fluctuation estimation section 1319 has post-Fourier-transform signal 1316 as input, finds modulated signal B channel fluctuation for carrier 1 through carrier 5 using modulated signal B pilot symbols 1201 in FIG. 13B, and outputs a modulated signal B channel fluctuation signal group 1320 (composed of estimation signals for carrier 1 through carrier 5).

A signal processing section 1321 has post-Fourier-transform signals 1306 and 1316, modulated signal A channel fluctuation signal groups 1308 and 1318, and modulated signal B channel fluctuation signal groups 1310 and 1320 as input, and by performing modulated signal A and B decoding, detection, and so forth, using these signals, obtains a modulated signal A digital signal 1322 and modulated signal B digital signal 1323.

Signal processing section 1321 may have the same kind of configuration as signal processing section 321 shown in FIG. 5. Thus, modulated signal A channel fluctuation estimation group 1308 is input instead of modulated signal A channel fluctuation signal 308 in FIG. 5, modulated signal B channel fluctuation estimation group 1310 is input instead of modulated signal B channel fluctuation signal 310, post-Fourier-transform signal 1306 is input instead of despread baseband signal 306, modulated signal A channel fluctuation estimation group 1318 is input instead of modulated signal A channel fluctuation signal 318, modulated signal B channel fluctuation estimation group 1320 is input instead of modulated signal B channel fluctuation signal 320, and post-Fourier-transform signal 1316 is input instead of despread baseband signal 316.

Assuming, for example, that separation section 507 has modulated signal A channel fluctuation estimation groups 501 and 504, modulated signal B channel fluctuation estimation groups 502 and 505, and post-Fourier-transform signals 503 and 506 as input, inverse matrix computation is executed for each carrier based on Equation (1), and modulated signal A estimated baseband signal 508 and modulated signal B estimated baseband signal 511 are output in accordance with the frequency-time axis frame configurations in FIG. 13A and FIG. 13B.

Then partial bit determination sections 509 and 512 determine partial bits in the same way as described above for each carrier. Signal point reduction sections 514 and 516 also perform signal point reduction in the same way as described above for each carrier, and likelihood detection section 518 also performs likelihood detection for each carrier. By this means, OFDM modulated signal A and B digital signals 1322 and 1323 are obtained. In this way, the present invention can also be implemented for a multicarrier system such as OFDM scheme.

Embodiment 2

In this embodiment, a method of signal point arrangement in the I-Q plane is described that simplifies division in the case of 2-bit partial determination and greatly improves reception quality compared with Embodiment 1. Although the description here mainly refers to modulated signal A, the same kind of processing can also be performed for modulated signal B.

The general configurations of a transmitting apparatus and receiving apparatus arc similar to those in Embodiment 1. Embodiment 2 differs from Embodiment 1 in the configuration of the modulation sections of the transmitting apparatus, and the configuration of the partial bit determination sections and signal point reduction sections of the receiving apparatus.

FIG. 15A shows a sample signal point arrangement by a transmitting apparatus of this embodiment, and FIG. 15B shows the partial bit determination method used by a receiving apparatus of this embodiment. That is to say, the kind of signal point mapping shown in FIG. 15A is performed by modulation sections 102 and 110 in FIG. 1 and modulation sections 1102 and 1112 in FIG. 12. Also, partial bits are determined by partial bit determination sections 509 and 512 in FIG. 5 by performing the kind of area division shown in FIG. 15B.

As shown in FIG. 15A, a modulation section of this embodiment takes 4 signal points as 1 set, and performs modulation processing (mapping) so that the distances between the 4 signal points in 1 set are small, but distances between sets are large. Also, a modulation section makes the distances between the 4 signal points in 1 set equal, and also makes the distances between sets equal. In this way, a modulation section arranges signal points so that an area can easily be divided into first through fourth quadrants.

By this means, 2 bits that are common within a set composed of 4 signal points can easily be demodulated on the receiving side. That is to say, since distances between signal points in a set are small and signal point distances between sets are large, the set (quadrant) in which a reception point is included can be determined easily and accurately, enabling 2-bit partial determination to be performed easily and accurately.

Specifically, when a received baseband signal is present in area 1 in the I-Q plane shown in FIG. 15B, the 2 bits Sa0=1 and Sa2=1 common to the 4 signal points of area 1 are determined to be partial bits; when a received baseband signal is present in area 2, the 2 bits Sa0=0 and Sa2=1 common to the 4 signal points of area 2 are determined to be partial bits; when a received baseband signal is present in area 3, the 2 bits Sa0=0 and Sa2=0 common to the 4 signal points of area 3 are determined to be partial bits; and when a received baseband signal is present in area 4, the 2 bits Sa0=1 and Sa2=0 common to the 4 signal points of area 4 are determined to be partial bits.

Partial bit determination section 509 in FIG. 5 outputs information of these determined 2 bits as modulated signal A determined partial bit information 510. The same kind of processing is also performed for modulated signal B by partial bit determination section 512.

Using the 4-bit information determined by partial bit determination sections 509 and 512, signal point reduction sections 514 and 516 in FIG. 5 reduce the 256 candidate signal points to 16 candidate signal points as described above in Embodiment 1.

Thus, according to this embodiment, in modulation sections 102, 110, 1102, and 1112 of transmitting apparatuses 100 and 1100, by performing signal point mapping of transmit bits whereby signal points are divided into a plurality of signal point sets on the IQ plane, and the minimum distance between signal points in a signal point set is made smaller than the minimum signal point distance between signal point sets, an effect can be obtained of enabling partial bit determination to be performed easily and accurately on the receiving side.

In addition, by making the distances between the 4 signal points in 1 set equal, and also making the distances between sets equal, the ratio of maximum transmit power to average transmit power is reduced. By this means, the linear amplifier requirements of the transmitting power amplifier are lessened, and an effect of enabling power consumption to be reduced is also obtained. The same is also true when this embodiment is applied to a 64-value modulation method.

In Embodiment 1 and this embodiment, a case has been described in which the signal point arrangements of modulated signal A and modulated signal B are the same, but similar effects can also be obtained when the signal point arrangements of modulated signal A and modulated signal B are different.

For example, on the transmitting side, the modulated signal A signal point arrangement may be set as shown in FIG. 15A, while the modulated signal B signal point arrangement is set as shown in FIG. 9A. Then, on the receiving side, a total of 3 bits are determined by determining 2 bits by means of partial bit determination section 509 for modulated signal A in FIG. 5, and determining 1 bit by means of partial bit determination section 512 for modulated signal B. Signal point reduction sections 514 and 516 then reduce the 256 candidate signal points to 32 signal points using this determined 3-bit partial bit information.

A method is also possible whereby only modulated signal A partial bits are determined on the receiving side. The configuration of signal processing section 321 for implementing this method is shown in FIG. 16. In this example, modulated signal A signal points are arranged as shown in FIG. 15A for ease of partial bit determination. Partial bit determination section 509 in FIG. 16 performs partial bit determination of 2 bits of modulated signal A based on the criteria in FIG. 15B. Signal point reduction sections 514 and 516 reduce the 256 candidate signal points to 64 candidate signal points using the determined 2 bits. Likelihood detection section 518 performs likelihood detection by finding the Euclidian distances between the 64 signal points and a received baseband signal.

Determining only partial bits for one modulated signal in this way enables the configuration of the partial bit determination section to be simplified, allowing the computational complexity to be reduced accordingly. This kind of configuration is particularly effective when a signal point arrangement is used whereby partial bit determination is easier for one modulated signal than for the other.

Embodiment 3

In this embodiment, an actual signal point arrangement method and partial bit determination method when using 64-value M-ary modulation as the modulation method are described. The general configurations of a transmitting apparatus and receiving apparatus are similar to those in Embodiment 1 and Embodiment 2, except that the modulation method is changed from modulation which has 16 signal points to modulation which has 64 signal points.

FIG. 17 shows the 64QAM signal point arrangement in the I-Q plane. A receiving apparatus of this embodiment, 1 bit is determined by each of partial bit determination sections 509 and 512 in FIG. 5 by performing area division so that the bit with the lowest probability of being erroneous among 6 bits is determined. Then the number of candidate signal points is reduced to 1024 by reducing 2-bit signal points from 64×64=4096 candidate signal points by signal point reduction sections 514 and 516. Likelihood detection section 518 performs likelihood detection by finding the Euclidian distances between each of the 1024 candidate signal points and a reception point.

Also, in the receiving apparatus, if area division is performed by partial bit determination sections 509 and 512 so that 2 bits are determined, and the respective 2-bit partial bits are determined, the number of candidate signal points can be reduced to 256. If area division is performed so that 3 bits are determined, and the respective 3-bit partial bits are determined, the number of candidate signal points can be reduced to 64. Furthermore, if area division is performed so that 4 bits are determined, and the respective 4-bit partial bits are determined, the number of candidate signal points can be reduced to 16. Thus, the greater the number of bits determined by partial bit determination sections 509 and 512 is made, the smaller the number of candidate signal points for performing likelihood detection can be made, enabling the amount of computation to be reduced. However, drawbacks are that the greater the number of bits determined by partial bit determination sections 509 and 512 is made, the more bit error rate performances degrade, and, as with 16QAM in Embodiment 1, the more complicated area division becomes.

Thus, in this embodiment, the kind of signal point arrangement shown in FIG. 18 is proposed as a more desirable 64-value M-ary modulation signal point arrangement. The basic concept of the signal point arrangement in FIG. 18 is the same as that described in Embodiment 2. That is to say, modulation processing (mapping) is performed whereby signal points are divided into a plurality of sets, and the minimum Euclidian distance between sets is made greater than the minimum Euclidian distance between signal points within a set.

Specifically, 16 signal points are taken as 1 set, and modulation processing (mapping) is performed so that the distances between the 16 signal points are small, but distances between sets are large. Also, a modulation section makes the distances between the 16 signal points in 1 set equal, and also makes the distances between sets equal. In this way, a modulation section arranges signal points so that an area can easily be divided into first through fourth quadrants.

By this means, 2 bits that are common within a set composed of 16 signal points can easily be demodulated on the receiving side. That is to say, since distances between signal points in a set are small and signal point distances between sets are large, the set (quadrant) in which a reception point is included can be determined easily and accurately, enabling 2-bit partial determination to be performed easily and accurately.

In this embodiment, the signal point arrangement shown in FIG. 19 is proposed as another desirable signal point arrangement for 64-value M-ary modulation. FIG. 19 shows a 64-value M-ary modulation signal point arrangement suitable for determining 4-bit partial bits for each modulated signal. The basic concept of this signal point arrangement, as in the case described above, is that modulation processing (mapping) is performed whereby signal points are divided into a plurality of sets, and the minimum Euclidian distance between sets is made greater than the minimum Euclidian distance between signal points within a set.

Specifically, 4 signal points are taken as 1 set, and modulation processing (mapping) is performed so that the distances between the 4 signal points within 1 set are small, but distances between sets are large. In this way, signal points are arranged so that an area can easily be divided into areas 1 through 16.

By this means, 4 bits that are common within a set composed of 16 signal points can easily be demodulated on the receiving side. That is to say, since distances between signal points in a set are small and signal point distances between sets are large, the set (area 1 to 16) in which a reception point is included can be determined easily and accurately, enabling 4-bit partial determination to be performed easily and accurately.

Thus, according to this embodiment, when different 64-value M-ary modulation signals are transmitted from a plurality of antennas, by performing modulation (mapping) processing whereby signal points of 64 values are divided into a plurality of sets, and the minimum Euclidian distance between sets is made larger than the minimum Euclidian distance between signal points in a set, easy and accurate partial bit determination processing and signal point reduction processing can be performed on the receiving side, enabling a received signal with good bit error rate performances to be obtained on the receiving side with a comparatively small computational complexity.

As also explained with regard to Embodiment 2, the method of this embodiment is not limited to a case in which the signal point arrangements of modulated signal A and modulated signal B are the same, and may also be implemented even in a case in which modulated signal A and modulated signal B signal points are arranged differently, and the number of partial bits determined for modulated signal A and modulated signal B are different.

Embodiment 4

In this embodiment, a soft decision value calculation method is described that is suitable for a case in which convolutional coding or turbo coding is performed on the transmitting side, and soft decision decoding is performed on the receiving side, in addition to implementation of the configurations in Embodiments 1 through 3. While this embodiment can basically be applied to cases in which any of the signal point arrangements described in the above embodiments are used, a case will be described here, by way of example, in which the signal point arrangement shown in FIG. 15A is implemented on the transmitting side.

FIG. 20, in which parts corresponding to those in FIG. 2 are assigned the same codes as in FIG. 2, shows the configuration of a transmitting apparatus of this embodiment. In transmitting apparatus 1900, a transmit digital signal 1901 is input to a coding section 1902. Coding section 1902 executes convolutional coding on transmit digital signal 1901 and thereby obtains a coded digital signal 101 and coded digital signal 109, and sends these signals to modulation sections 102 and 110.

The overall configuration of a receiving apparatus is as shown in FIG. 4. In this embodiment, signal processing section 321 in FIG. 4 is configured as signal processing section 2000 in FIG. 21. Parts in FIG. 21 corresponding to those in FIG. 5 are assigned the same codes as in FIG. 5.

Signal processing section 2000 of this embodiment has a soft decision value calculation section 2001. Soft decision value calculation section 2001 has post-reduction signal point information 515 and 517, and despread baseband signals 503 and 506, as input, obtains soft decision value signal 2002 using these signals, and sends soft decision value signal 2002 to determination section 2003. Determination section 2003 obtains digital signal 2004 by decoding soft decision value signal 2002.

The processing performed by soft decision value calculation section 2001 and determination section 2003 will be described using FIG. 22.

Assume, for example, that transmitting apparatus 1900 in FIG. 20 transmits modulated signals using the kind of signal point arrangement shown in FIG. 15A, and that receiving apparatus 300 has received these modulated signals.

Then, in signal processing section 2000 in FIG. 21, partial bit determination section 509 determines 2 bits Sa0 and Sa2 of modulated signal A based on the area divisions in the signal point arrangement in FIG. 15B, and outputs these as partial bit information 510, and similarly, partial bit determination section 512 determines 2 bits Sb0 and Sb2 of modulated signal B based on the area divisions in the signal point arrangement in FIG. 15B, and outputs these as partial bit information 513.

Using the 4-bit information from partial bit determination sections 509 and 512, signal point reduction section 514 finds 16 signal points from 16×16=256 signal points, and sends these to soft decision value calculation section 2001 as post-reduction signal point information 515. Similarly, signal point reduction section 516 sends 16-signal-point information to soft decision value calculation section 2001 as post-reduction signal point information 517.

Here, as an example, it is assumed that the modulated signal A partial bits determined by partial bit determination section 509 are Sa0=0 and Sa2=0, and the modulated signal B partial bits determined by partial bit determination section 512 are Sb0=0 and Sb2=0. At this time, soft decision value calculation section 2001 performs the calculations in FIG. 22 using post-reduction signal point information 515 and despread baseband signal 316.

(Step ST1)

First, the squares, for example, of the Euclidian distances between the 16 signal points of post-reduction signal point information 515 and the despread baseband signals are found. Here, the squares of Euclidian distances are represented by the function D(Sa0, Sa2, Sb0, Sb2, Sa1, Sa3, Sb1, Sb3). Then, since Sa0=0, Sa2=0, Sb0=0, and Sb2=0 in this example, 16 values are found for which Sa1, Sa3, Sb1, and Sb3 are 0 or 1 in D(0, 0, 0, 0, Sa1, Sa3, Sb1, Sb3). Posterior probability can also be found using this.

(Step ST2)

Next, the maximum value is found from the 16 values of D(0, 0, 0, 0, Sa1, Sa3, Sb1, Sb3). The maximum value at this time is designated Dmax.

(Step ST3)

Lastly, the values of the squares of the Euclidian distances of the 240 signal points other than the 16 signal points for which the square of the Euclidian distance has actually been found are all taken to be Dmax. In this example, the values from D(0, 0, 0, 1, 0, 0, 0, 0) to D(1, 1, 1, 1, 1, 1, 1, 1) are all taken to be Dmax. That is to say, since the Euclidian distances to the 240 signal points other than the 16 signal points for which the square of the Euclidian distance has actually been found can be considered to be greater than the maximum value of the squares of the Euclidian distances of the 16 signal points, Dmax, the squares of the Euclidian distances of these signal points are uniformly set to Dmax. By this means, the squares of the Euclidian distances of 256 points can easily be obtained by making effective use of the squares of the Euclidian distances of 16 signal points.

Then soft decision value calculation section 2001 outputs the value of the square of the Euclidian distances of these 256 points (branch metric) as soft decision value signal 2002.

Determination section 2003 has soft decision value signal 2002 as input, finds a path metric from the branch metric, decodes this, and outputs digital signal 2004.

Thus, according to signal processing section 2000, a soft decision value can easily be obtained for all candidate signal points by obtaining soft decision values for all candidate signal points by calculating only the Euclidian distances between reduced candidate signal points and a reception point, and setting all the Euclidian distances between other signal points and the reception point as maximum value Dmax of the aforementioned found Euclidian distances.

FIG. 23, in which parts corresponding to those in FIG. 21 are assigned the same codes as in FIG. 21, shows another configuration of a signal processing section of this embodiment. Signal processing section 2200 has a weighting factor calculation section 2201.

Weighting factor calculation section 2201 has modulated signal A channel fluctuation signals 308 and 318, and modulated signal B channel fluctuation signals 310 and 320, as input, and finds a weighting factor corresponding to a degree of reliability that is multiplied by a branch metric. Here, when separation section 507 separates signals by performing the computations in Equation (1), for example, it is sufficient for weighting factor calculation section 2201 to find a weighting factor corresponding to the precision of signal separation. Specifically, weighting factor calculation section 2201 can find the minimum power of an eigenvalue of the matrix in Equation (1), for example, as shown in “Soft-decision decoder employing eigenvalue of channel matrix in MIMO systems” IEEE PIMRC2003, pp. 1703-1707, September 2003, and output this as a weighting factor signal 2202.

Soft decision value calculation section 2001 has post-reduction signal point information 515 and 517, despread baseband signals 306 and 316, and weighting factor signal 2202 as input, and obtains soft decision value signal 2002 by multiplying a found branch metric by a weighting factor.

Multiplying a branch metric by a weighting factor in signal processing section 2200 in this way enables bit error rate performances to be greatly improved. In the above description, a case has been referred to in which the minimum power of an eigenvalue is used as a weighting factor, but a weighting factor is not limited to this.

Also, in this embodiment, a case has been described in which convolutional coding is used, but this embodiment is not limited to this case, and can also be similarly implemented in a case in which turbo coding, low-density parity coding, or the like is used. Furthermore, this embodiment can also be similarly implemented when a function such as interleaving, which changes the signal order, or puncturing, which performs partial signal elimination and reduces redundancy, is provided. This is also true for other embodiments.

Also, in this embodiment, an example has been described in which the squares of Euclidian distances are found and a soft decision value is found on this basis, but this embodiment can also be applied to a case in which a soft decision value is found on the basis of a different likelihood. This also applies to other embodiments. Furthermore, apart from the method of finding a soft decision value described in this embodiment, a method may be used whereby the SNR after separation is found using step S1, and taking this as a prior probability, a soft decision value is found using a prior probability and posterior probability. This also applies to other embodiments.

Embodiment 5

In this embodiment, a more suitable coding (convolutional coding or turbo coding) method is described for use when performing processing that reduces candidate signal points by partial bit reduction on the receiving side as described in the above embodiments.

The general configuration of a transmitting apparatus is as shown in FIG. 20. In this embodiment, it is assumed by way of example that modulation sections 102 and 110 perform modulation which has 16 signal points using the kind of signal point arrangement shown in FIG. 15A. The general configuration of a receiving apparatus is as shown in FIG. 4.

FIG. 24 shows the configuration of a coding section of this embodiment. That is to say, coding section 2300 in FIG. 24 is used as coding section 1902 in FIG. 20. Coding section 2300 has (Sa0, Sa2) coding section 2302, (Sa1, Sa3, Sb1, Sb3) coding section 2304, and (Sb0, Sb2) coding section 2306. Coding sections 2302, 2304, and 2306 have digital signal 1901 as input, and perform coding processing on the respective specific bits.

That is to say, (Sa0, Sa2) coding section 2302 codes bits Sa0 and Sa2 contained in digital signal 1901, and outputs bit Sa0 and Sa2 coding information 2303; (Sa1, Sa3, Sb1, Sb3) coding section 2304 codes bits Sa1, Sa3, Sb1, and Sb3 contained in digital signal 1901, and outputs bit Sa1, Sa3, Sb1, and Sb3 coding information 2305; and (Sb0, Sb2) coding section 2306 codes bits Sb0 and Sb2 contained in digital signal 1901, and outputs bit Sb0 and Sb2 coding information 2307.

Executing coding processing in predetermined bit units in this way enables error correction decoding processing to be performed in those bit units on the receiving side. A particular aspect of the suitability of this embodiment is that performing coding processing in bit units for which partial bit determination is performed on the receiving side enables error correction decoding processing to be performed in partial bit units.

(Sa0, Sa1, Sa2, Sa3) signal generation section 2308 has Sa0 and Sa2 coding information 2303 and Sa1, Sa3, Sb1, and Sb3 coding information 2305 as input, generates Sa0, Sa1 Sa2, and Sa3 signals, and outputs these as coded digital signal 101.

Similarly, (Sb0, Sb1, Sb2, Sb3) signal generation section 2310 has Sa1, Sa3, Sb1, and Sb3 coding information 2305 and Sb0 and Sb2 coding information 2307 as input, generates Sb0, Sb1, Sb2, and Sb3 signals, and outputs these as coded digital signal 109.

Next, the configuration of a receiving apparatus that receives such transmit signals will be described. The general configuration of a receiving apparatus of this embodiment is as shown in FIG. 4. The configuration of signal processing section 321 of receiving apparatus 300 is as shown in FIG. 5. In this embodiment, partial bit determination section 509 of signal processing section 321 is configured as shown in FIG. 25A, partial bit determination section 512 is configured as shown in FIG. 25B, and likelihood detection section 518 is configured as shown in FIG. 25C.

(Sa0, Sa2) decoding section 2402 in FIG. 25A has modulated signal A estimated baseband signal 508 as input, obtains decoded bits Sa0 and Sa2 by decoding this signal, and outputs these bits as modulated signal A determined partial bit information 510.

(Sb0, Sb2) decoding section 2405 in FIG. 25B has modulated signal B estimated baseband signal 511 as input, obtains decoded bits Sb0 and Sb2 by decoding this signal, and outputs these bits as modulated signal B determined partial bit information 513.

Implementing error correction coding in partial bit units in this way enables reception quality to be greatly improved. That is to say, if there is an error in partial bit determination, an erroneous signal point is selected during signal point reduction, and therefore the probability of an error occurring in determination of the remaining bits is extremely high. In contrast, in this embodiment, the implementation of error correction coding in partial bit units enables the possibility of being able to decode partial bits correctly to be increased, enabling the possibility of selecting an erroneous signal point during signal point reduction to be decreased.

It is still more desirable for coding with higher error correction capability than (Sa1, Sa3, Sb1, Sb3) coding section 2304 to be performed by (Sa0, Sa2) coding section 2302 and (Sb0, Sb2) coding section 2306. This enables the possibility of being able to decode partial bits Sa0, Sa2, Sb0, and Sb2 without error to be greatly increased, enabling the possibility of performing erroneous signal point reduction to be greatly reduced, with the result that bit error rate performances can be significantly improved.

As modulation signal point arrangements which has 16 signal points, the kind of signal point arrangements shown in FIG. 15A and FIG. 15B are more suitable for implementation of the kind of error correction coding of this embodiment than 16QAM. This is because, whereas the determined partial bits differ according to the area in 16QAM, in the cases shown in FIG. 15A and FIG. 15B the partial bits are fixed at (Sa0, Sa2) and (Sb0, Sb2) irrespective of the area, enabling error correction coding to be implemented easily. In this embodiment, an example has been described in which error correction coding is implemented for modulation which has 16 signal points, but the same kind of effect as in this embodiment can also be obtained if the same kind of error correction coding processing as in this embodiment is performed for 64-value M-ary modulation. In this case, also, for the same reasons as stated above, use of the kind of signal point arrangements shown in FIG. 18 and FIG. 19 is more suitable than 64QAM in enabling error correction coding to be implemented easily.

(Sa1, Sa3, Sb1, Sb3) decoding section 2411 in FIG. 25C has post-reduction signal point information 515 and 517, and despread baseband signals 316 and 306, as input, finds a branch metric by finding, for example, the squares of the Euclidian distances between candidate signal points and baseband signals, finds a path metric from the branch metric, and performs decoding, thereby obtaining modulated signal A received digital signal 322 and modulated signal B received digital signal 323.

Thus, according to this embodiment, by executing coding processing with partial bits as a coding unit—that is, coding transmit bits mapped within the same signal point set together—in addition to implementation of the configurations in Embodiments 1 through 4, it is possible to greatly improve bit error rate performances on the receiving side in addition to obtaining the effects of Embodiments 1 through 4.

Also, by executing coding processing with higher error correction capability for partial bits than for other bits—that is, coding transmit bits mapped within the same signal point set together—bit error rate performances on the receiving side can be further improved.

In this embodiment, a case has been described in which the transmitting-side coding section is configured as shown in FIG. 24, and the receiving-side signal processing section is configured as shown in FIG. 5, FIG. 25A, FIG. 25B, and FIG. 25C, but the coding section and signal processing section configurations are not limited to these. FIG. 26 shows another example of a coding section configuration, and FIG. 27 shows another example of a signal processing section configuration.

In FIG. 26, in which parts corresponding to those in FIG. 24 are assigned the same codes as in FIG. 24, coding section 2500 has an (Sa0, Sa2) coding section 2302, an (Sa1, Sa3) coding section 2501, an (Sb0, Sb2) coding section 2306, and an (Sb1, Sb3) coding section 2503. Coding sections 2302, 2501; 2306, and 2503 have digital signal 1901 as input, and perform coding processing on the respective specific bits.

That is to say, (Sa0, Sa2) coding section 2302 codes bits Sa0 and Sa2 contained in digital signal 1901, and outputs bit Sa0 and Sa2 coding information 2303; (Sa1, Sa3) coding section 2501 codes bits Sa1 and Sa3 contained in digital signal 1901, and outputs bit Sa1 and Sa3 coding information 2502; (Sb0, Sb2) coding section 2306 codes bits Sb0 and Sb2 contained in digital signal 1901, and outputs bit Sb0 and Sb2 coding information 2307; and (Sb1, Sb3) coding section 2503 codes bits Sb1 and Sb3 contained in digital signal 1901, and outputs bit Sb1 and Sb3 coding information 2504.

(Sa0, Sa1, Sa2, Sa3) signal generation section 2308 has Sa0 and Sa2 coding information 2303 and Sa1, Sa3 coding information 2502 as input, generates Sa0, Sa1, Sa2, and Sa3 signals, and outputs these as coded digital signal 101.

Similarly, (Sb0, Sb1, Sb2, Sb3) signal generation section 2310 has Sb1 and Sb3 coding information 2504 and Sb0 and Sb2 coding information 2307 as input, generates Sb0, Sb1, Sb2, and Sb3 signals, and outputs these as coded digital signal 109.

Next, the configuration of signal processing section 2600 in FIG. 27 will be described. Signal processing section 2600 in FIG. 27 has a similar configuration to signal processing section 321 in FIG. 5, except that, as compared with signal processing section 321 in FIG. 5, soft decision decoding sections 2601 and 2602 are provided as partial bit determination sections 509 and 512 (that is, partial bit demodulation section 2610 is composed of separation section 507 and soft decision decoding sections 2601 and 2602), and hard decision decoding sections 2606 and 2608 are provided. Soft decision decoding section 2601 has modulated signal A estimated baseband signal 508 as input, performs soft decision decoding for partial bits Sa0 and Sa2 in FIG. 26, and outputs partial bit Sa0 and Sa2 information thus obtained as modulated signal A determined partial bit information 510. Similarly, soft decision decoding section 2602 has modulated signal B estimated baseband signal 511 as input, performs soft decision decoding for partial bits Sb0 and Sb2 in FIG. 26, and outputs partial bit Sb0 and Sb2 information thus obtained as modulated signal B determined partial bit information 513.

Signal point reduction sections 514 and 516 perform candidate signal point reduction using determined partial bit information 510 and 513, and send post-reduction signal point information 515 and 517 to likelihood determination section 2603.

Likelihood determination section 2603 performs likelihood determination of the candidate signal points with the highest likelihood from the post-reduction candidate signal points and despread baseband signal 1316, and finds bits Sa1, Sa3, Sb1, and Sb3. Then likelihood determination section 2603 sends bits Sa1 and Sa3 to hard decision decoding section 2606 as bit information 2604, and sends bits Sb1 and Sb3 to hard decision decoding section 2608 as bit information 2605.

Hard decision decoding section 2606 obtains modulated signal A post-error-correction bit information 2607 by performing hard decision decoding of bit information 2604. Similarly, hard decision decoding section 2608 obtains modulated signal B post-error-correction bit information 2609 by performing hard decision decoding of bit information 2605.

Here, modulated signal A determined partial bit information 510 and modulated signal A post-error-correction bit information 2607 correspond to final post-error-correction modulated signal A bit information, and modulated signal B determined partial bit information 513 and modulated signal B post-error-correction bit information 2609 correspond to final post-error-correction modulated signal B bit information.

Thus, in signal processing section 2600, by providing soft decision decoding sections 2601 and 2602, and finding partial bits used in signal point reduction by means of soft decision decoding processing, the probability of error of partial bits can be reduced compared with a case in which hard decision processing is performed, for example, enabling the final bit error rate performances to be improved. The reason for performing hard decision processing on signals after likelihood determination is that, since determination is carried out for modulated signal A and modulated signal B simultaneously when likelihood determination is performed, in principal it is difficult to make a soft decision for only modulated signal A or to make a soft decision for only modulated signal B.

In this embodiment, a case has been described in which coding is performed on bits (Sa1, Sa3, Sb1, Sb3) other than the bits for which partial bit determination is performed on the receiving side, but it is also possible for coding not to be performed for bits other than the bits for which partial bit determination is performed. Essentially, the same kind of effect as in this embodiment can be obtained as long as coding is performed in partial bit units.

Embodiment 6

In this embodiment, the implementation of trellis coding modulation on the transmitting side is proposed. A case in which 16QAM is used as the modulation method will be described here by way of example.

The general configuration of a transmitting apparatus is as shown in FIG. 2, and the transmit signal frame configurations are as shown in FIG. 3. The general configuration of a receiving apparatus is as shown in FIG. 4, and the detailed configuration of signal processing section 321 in FIG. 4 is as shown in FIG. 5.

In order to implement 16QAM trellis coding modulation, modulation sections 102 and 110 of transmitting apparatus 100 in FIG. 2 can be configured as shown in FIG. 28, for example.

In FIG. 28, reference codes 2701, 2702, and 2703 denote shift registers and reference codes 2704 and 2705 denote exclusive OR circuits, and b0, b1, b2, and b3 are generated from inputs a0, a1, and a2. A baseband signal generation section 2706 has b0, b1, b2, and b3 as input, and obtains a baseband signal 2707 by performing 16QAM mapping.

The operation of a receiving apparatus will now be described. As described above, the characteristic operation of a receiving apparatus of the present invention lies in partial bit determination sections 509 and 512 (FIG. 5). Since similar operations are performed by partial bit determination section 509 and partial bit determination section 512, the operation of partial bit determination section 509 will mainly be described here.

Partial bit determination section 509 has modulated signal A estimated baseband signal 508 as input, determines coding related bits—that is, b0, b1, and b2 in FIG. 28—by performing Viterbi decoding, for example, and outputs this information as modulated signal A determined partial bit information 510. Similarly, partial bit determination section 512 outputs modulated signal B determined partial bit information 513 (3-bit information).

Signal point reduction sections 514 and 516 perform signal point reduction. Then likelihood detection section 518 determines b3 information in FIG. 28 transmitted by modulated signal A, and b3 information in FIG. 28 transmitted by modulated signal B, and outputs this information as a modulated signal A digital signal 519 and modulated signal B digital signal 520.

Thus, according to this embodiment, performing trellis coding modulation on the transmitting side enables implementation of error correction coding to be carried out easily, and bit error rate performances on the receiving side to be effectively improved with a simple transmitting apparatus configuration.

Embodiment 7

In this embodiment, an actual sample configuration when using 3 receiving antennas and 3 transmitting antennas will be described as an example of a case in which the number of transmitting antennas and the number of receiving antennas are greater than two.

Also, in this embodiment, a partial bit determination method and signal point reduction method for effectively improving bit error rate performances are proposed.

FIG. 30, in which parts corresponding to those in FIG. 2 are assigned the same codes as in FIG. 2, shows the configuration of a transmitting apparatus according to this embodiment. Transmitting apparatus 2900 has the same kind of configuration as transmitting apparatus 100 in FIG. 2, except for the fact that it has a transmitting section that transmits a modulated signal C in addition to those transmitting modulated signal A and modulated signal B. Here, only the configuration of the transmitting section that transmits modulated signal C will be described.

Modulation section 2902 has a digital signal 2901 and frame configuration signal 118 as input, modulates digital signal 2901 in accordance with frame configuration signal 118, and sends a baseband signal 2903 thus obtained to a spreading section 2904. Spreading section 2904 multiplies baseband signal 2903 by a spreading code, and sends a spread baseband signal 2905 thus obtained to a radio section 2906. Radio section 2906 executes frequency conversion, amplification, and so forth on spread baseband signal 2905, thereby obtaining a modulated signal 2907 (modulated signal C). Modulated signal 2907 is output as a radio wave from an antenna 2908.

Frame configuration signal generation section 117 outputs information on the frame configurations in FIG. 31, for example, as frame configuration signal 118.

FIG. 31 shows sample frame configurations of modulated signals transmitted from antennas 108, 116, and 2908 of transmitting apparatus 2900. Modulated signal A transmitted from antenna 108, modulated signal B transmitted from antenna 116, and modulated signal C transmitted from antenna 2908 have channel estimation symbols 201, 203, and 3001 for channel estimation, and data symbols 202, 204, and 3002. Transmitting apparatus 2900 transmits modulated signal A, modulated signal B, and modulated signal C with the frame configurations shown in FIG. 31 at virtually the same time. Channel estimation symbols 201, 203, and 3001 for channel estimation can also be referred to as pilot symbols, unique words, or preambles.

FIG. 32, in which parts corresponding to those in FIG. 4 are assigned the same codes as in FIG. 4, shows the configuration of a receiving apparatus according to this embodiment. Descriptions of parts that operate in the same way as in FIG. 4 are omitted from the following explanation.

If, in transmitting apparatus 2900 in FIG. 30, a signal transmitted from antenna 108 is designated Txa(t), a signal transmitted from antenna 116, Txb(t), and a signal transmitted from antenna 2908, Txc (t); and in receiving apparatus 3100 in FIG. 32, a signal received by antenna 301 is designated Rx1(t), a signal received by antenna 311, Rx2(t), and a signal received by antenna 3105, Rx3(t); and, furthermore, propagation fluctuations between the transmitting and receiving antennas are designated h11(t) h12(t), h13(t), h21(t), h22(t), h23(t), h31(t), h32(t), and h33(t); then the relational expression in the following equation holds true, where t denotes time.

$\begin{matrix} {\begin{pmatrix} {{Rx}\; 1(t)} \\ {{Rx}\; 2(t)} \\ {{Rx}\; 3(t)} \end{pmatrix} = {\begin{pmatrix} {h\; 11(t)} & {h\; 12(t)} & {h\; 13(t)} \\ {h\; 21(t)} & {h\; 22(t)} & {h\; 23(t)} \\ {h\; 31(t)} & {h\; 32(t)} & {h\; 33(t)} \end{pmatrix}\begin{pmatrix} {{Txa}(t)} \\ {{Txb}(t)} \\ {{Txc}(t)} \end{pmatrix}}} & (2) \end{matrix}$

A modulated signal C channel fluctuation estimation section 3101 has despread baseband signal 306 as input, estimates channel fluctuation using modulated signal C channel estimation symbol 3001 in the frame configuration in FIG. 31, for example, and sends a modulated signal C channel fluctuation signal 3102 thus obtained to a signal processing section 3117. Similarly, a modulated signal C channel fluctuation estimation section 3103 has despread baseband signal 316 as input, estimates channel fluctuation using modulated signal C channel estimation symbol 3001 in the frame configuration in FIG. 31, for example, and sends a modulated signal C channel fluctuation signal 3104 thus obtained to signal processing section 3117.

A radio section 3107 has a received signal 3106 received by antenna 3105 as input, executes frequency conversion, quadrature demodulation, and so forth on received signal 3106, and sends a baseband signal 3108 thus obtained to a despreading section 3109. Despreading section 3109 despreads baseband signal 3108, and outputs a despread baseband signal 3110 thus obtained.

A modulated signal A channel fluctuation estimation section 3111 has despread baseband signal 3110 as input, estimates channel fluctuation using modulated signal A channel estimation symbol 201 in the frame configuration in FIG. 31, for example, and sends a modulated signal A channel fluctuation signal 3112 thus obtained to signal processing section 3117. Similarly, a modulated signal B channel fluctuation estimation section 3113 has despread baseband signal 3110 as input, estimates channel fluctuation using modulated signal B channel estimation symbol 203 in the frame configuration in FIG. 31, for example, and sends a modulated signal B channel fluctuation signal 3114 thus obtained to signal processing section 3117. In the same way, a modulated signal C channel fluctuation estimation section 3115 has despread baseband signal 3110 as input, estimates channel fluctuation using modulated signal C channel estimation symbol 3001 in the frame configuration in FIG. 31, for example, and sends a modulated signal C channel fluctuation signal 3116 thus obtained to signal processing section 3117.

Signal processing section 3117 has despread baseband signals 306, 316, and 3110, modulated signal A channel fluctuation signals 308, 318, and 3112, modulated signal B channel fluctuation signals 310, 320, and 3114 and modulated signal C channel fluctuation signals 3102, 3104, and 3116, as input, and by performing modulated signal A, B, and C detection, decoding, and so forth, using these signals, obtains a modulated signal A digital signal 322, modulated signal B digital signal 323, and modulated signal C digital signal 3118.

A sample configuration of signal processing section 3117 is shown in FIG. 33, and another sample configuration of signal processing section 3117 is shown in FIG. 34.

First, the configuration in FIG. 33 will be described. In FIG. 33, in which parts corresponding to those in FIG. 5 are assigned the same codes as in FIG. 5, separation section 3201 of partial bit demodulation section 3230 of signal processing section 3117 has modulated signal A channel fluctuation signals 308, 318, and 3112, modulated signal B channel fluctuation signals 310, 320, and 3114, modulated signal C channel fluctuation signals 3102, 3104, and 3116, and despread baseband signals 306, 316, and 3110 as input, and obtains transmit signals Txa(t), Txb(t), and Txc(t) by performing an inverse matrix computation or MMSE (Minimum Mean Square Error) computation, for example, for Equation (2). Separation section 3201 sends thus obtained modulated signal A estimated baseband signal 508 to partial bit determination section 509, modulated signal B estimated baseband signal 511 to partial bit determination section 512, and modulated signal C estimated baseband signal 3207 to partial bit determination section 3208. Partial bit determination sections 509, 512, and 3208 send out found partial bit information 510, 512, and 3209.

Partial bit determination of partial bit determination sections 509, 512, and 3208 can be performed by using the methods in FIG. 9B and FIG. 11B above, for example, when the modulation method is 16QAM. In the case of QPSK, partial bit determination can be implemented by performing the kind of area division shown in FIG. 29, for example. Here, an implementation method in the case of 3 antennas will be described taking a case in which the modulation method is 16QAM, and 2 of 4 bits are determined as in FIG. 11B, as an example.

When three 16QAM signals transmitted simultaneously from different antennas are received, 16×16×16=4096 candidate signal points exist. As 2 bits are determined for each of modulated signals A, B, and C by partial bit determination sections 509, 512, and 3208, the 4096 signal points are reduced to 4096/4/4/4=64 candidate signal points. Thus, in likelihood detection section 3212, branch metrics between 64 candidate signal points and despread baseband signals are found, and by performing narrowing-down to one candidate signal point and detection, modulated signal A, modulated signal B, and modulated signal C digital signals 322, 323, and 3213 are obtained.

By thus also performing partial bit determination, reducing the number of candidate signal points using determined partial bits, and performing likelihood determination using the reduced candidate signal points even when there are 3 transmitting antennas, 3 receiving antennas, and 3 transmit modulated signals, in the same way as when there are 2 transmitting antennas, 2 receiving antennas, and 2 transmit modulated signals, received digital signals 322, 323, and 3213 of good reception quality can be obtained with a comparatively small amount of computation.

Next, the configuration in FIG. 34 will be described. Signal processing section 3117 in FIG. 34, in which parts corresponding to those in FIG. 33 are assigned the same codes as in FIG. 33, has a control section 3301.

Control section 3301 has modulated signal A channel fluctuation signals 308, 318, and 3112, modulated signal B channel fluctuation signals 310, 320, and 3114, and modulated signal C channel fluctuation signals 3102, 3104, and 3116 as input, and estimates, for example, the received field strength of modulated signal A, the received field strength of modulated signal B, and the received field strength of modulated signal C. Control section 3301 then outputs control information 3302 such that partial bit determination is not performed for only the modulated signal with the lowest field strength.

Assume, for example, that the received field strength of modulated signal A is the lowest. In this case, modulated signal A partial bit determination section 509 is controlled so as not to perform bit determination. That is to say, determined bits are 0 bits. On the other hand, modulated signal B partial bit determination section 512 and modulated signal C partial bit determination section 3208 are each controlled so as to perform 2-bit determination. Then signal point reduction sections 514, 516, and 3210 reduce the 4096 candidate signal points to 4096/4/4=256 candidate signal points using 0 modulated signal A determined bits (that is to say, no bits have been determined), 2 modulated signal B determined bits, and 2 modulated signal C determined bits. In likelihood detection section 3212, branch metrics between 256 candidate signal points and despread baseband signals are found, and by performing narrowing-down to one candidate signal point and detection, modulated signal A, modulated signal B, and modulated signal C digital signals 322, 323, and 3213 are obtained.

By selecting which modulated signals' partial bits are used for signal point reduction in this way, received digital signals with significantly better bit error rate performances can be obtained than in a case in which partial bits of all modulated signals are simply used for signal point reduction (as in the configuration in FIG. 33, for example).

That is to say, when candidate signal point reduction is performed simply by using the results of partial bit determination for all modulated signals, the probability of error of partial bit determination results for a modulated signal of low reception quality (in the case of this embodiment, received field strength) increases, and in line with this, the probability of not being able to perform candidate signal point reduction accurately also increases. As a result, there is a risk of degradation of the bit error rate performances of the final received digital signals. Taking this into consideration, in this embodiment signal point reduction is performed using only partial bit determination results of modulated signals that have good reception quality.

Thus, according to this embodiment, by providing a control section 3301 that controls which modulated signals' partial bits are used for candidate signal point reduction by signal point reduction sections 514, 516, and 3210 based on the reception quality of each modulated signal, received digital signals 322, 323, and 3213 with significantly better bit error rate performances can be obtained.

In this embodiment, a case in which received field strength is used as a reception quality parameter has been described as an example, but this is not a limitation, and it is also possible, for example, to find the carrier power to noise power ratio of each modulated signal after inverse matrix computation or MMSE computation, and use this as a reception quality parameter for each modulated signal.

Also, in this embodiment an example has been described in which partial bits are determined for only two modulated signals, but the present invention can be similarly implemented by determining partial bits for only one modulated signal.

Furthermore, the number of bits determined as partial bits may be varied according to a reception quality priority order. For example, compatibility between good bit error rate performances and a small computation scale can be achieved by having 2 bits determined by the modulated signal A partial bit determination section, 1 bit determined by the modulated signal B partial bit determination section, and 0 bits determined by the modulated signal C partial bit determination section when the relationship “modulated signal A received field strength>modulated signal B received field strength>modulated signal C received field strength” holds true.

That is to say, if the number of partial bits used in each modulated signal is controlled by control section 3301 in signal point reduction by signal point reduction sections 514, 516, and 3210 based on the reception quality of each modulated signal, received digital signals 322, 323, and 3213 with significantly better bit error rate performances can be obtained.

In this embodiment, a case has been described in which 16QAM is used as the modulation method, but the same kind of effect can also be obtained when a different modulation method is used.

Also, in this embodiment, a case in which the number of transmitting antennas is 3, the number of receiving antennas is 3, and the number of transmit modulated signals is 3 has been described as an example, but this embodiment can be widely applied to cases with n transmitting antennas, n receiving antennas, and n transmit signals (where n>2). For example, in a case in which the number of transmitting antennas is 2, the number of receiving antennas is 2, and the number of transmit modulated signals is 2, if modulated signal A received field strength>modulated signal B received field strength, determination may be carried out whereby 2 partial bits are determined for modulated signal A, 1-bit or 0-bit partial determination is performed for modulated signal B, and the remaining bits are then included by performing likelihood determination.

Furthermore, in this embodiment, a case in which coding is not performed has been described as an example, but the same kind of effect can also be obtained by using the determination method of this embodiment when error correction coding is applied.

A method may also be used whereby modulated signal A, modulated signal B, and modulated signal C received digital signals 322, 323, and 3213 are obtained by determining partial bits of modulated signal A and modulated signal B and obtaining branch metric BM_(AB) from candidate signal points reduced using these partial bits, determining partial bits of modulated signal A and modulated signal C and obtaining branch metric BM_(AC) from candidate signal points reduced using these partial bits, and determining partial bits of modulated signal B and modulated signal C and obtaining branch metric BM_(BC) from candidate signal points reduced using these partial bits, and performing determination using these branch metrics BM_(AB), BM_(AC), and BM_(BC).

As a result of performing a simulation, it was found that the method described in this embodiment, whereby partial bits used in candidate signal point reduction by signal point reduction sections are controlled according to the reception quality of each modulated signal, enables received digital signals 322, 323, and 3213 with extremely good bit error rate performances to be obtained especially when MMSE is performed by separation section 3201 (FIG. 34).

Embodiment 8

In above Embodiment 1, a 1-bit partial determination method when the modulation method is 16QAM (FIG. 9B) was described, but in this embodiment, a 1-bit partial determination method will be described that enables significantly better bit error rate performances to be obtained.

FIG. 35 shows an example of 16QAM signal point arrangement and a received-signal signal point. In this figure, reference codes 3401 through 3416 denote 16QAM signal points (candidate signal points), and reference code 3417 denotes a received-signal signal point (reception point). FIG. 35 also shows the relationships of the 4 bits (S0, S1, S2, S3) of signal points 3401 through 3416.

In a 1-bit partial bit determination method of this embodiment, first, the Euclidian distances between received-signal signal point 3417 and 16 QAM signal points 3401 through 3416 are found, the 16QAM signal point with the minimum Euclidian distance is found, and the 4 bits indicated by that signal point are found. In the example in FIG. 35, signal point 3407 is detected as the signal point having the minimum Euclidian distance from reception point 3417, and (S0, S1, S2, S3)=(1, 1, 1, 1) is found as the 4-bit bit string indicated by that signal point 3407.

Next, the following Euclidian distances are found for the 4 bits (S0, S1, S2, S3).

As “1” has been found for bit S0, signal points with “0” in the S0 position of bit string (S0, S1, S2, S3) are searched for. As a result of the search, signal points 3401, 3402, 3405, 3406, 3409, 3410, 3413, and 3414 are obtained. Then the minimum Euclidian distance between these 8 signal points and reception point 3417 is found, and the value of minimum Euclidian distance D_(min,S0) is found.

Similarly, as “1” has been found for bit S1, signal points with “0” in the S1 position of bit string (S0, S1, S2, S3) are searched for. As a result of the search, signal points 3401, 3404, 3405, 3408, 3409, 3412, 3413, and 3416 are obtained. Then the minimum Euclidian distance between these 8 signal points and reception point 3417 is found, and the value of minimum Euclidian distance D_(min,S1) is found.

Similarly, as “1” has been found for bit S2, signal points with “0” in the S2 position of bit string (S0, S1, S2, S3) are searched for. As a result of the search, signal points 3409, 3410, 3411, 3412, 3413, 3414, 3415, and 3416 are obtained. Then the minimum Euclidian distance between these 8 signal points and reception point 3417 is found, and the value of minimum Euclidian distance D_(min,S2) is found.

Similarly, as “1” has been found for bit S3, signal points with “0” in the S3 position of bit string (S0, S1, S2, S3) are searched for. As a result of the search, signal points 3401, 3402, 3403, 3404, 3413, 3414, 3415, and 3416 are obtained. Then the minimum Euclidian distance between these 8 signal points and reception point 3417 is found, and the value of minimum Euclidian distance D_(min,S3) is found.

That is to say, signal points that have a value that is the NOT of determined bit Sx are searched for, the minimum Euclidian distance between these signal points and reception point 3407 is found, and the value of minimum Euclidian distance D_(min,Sx) is found.

Then the item with the maximum value among Dmin,S0, D_(min,s1), D_(min,S2), and D_(min,S3) is searched for. If, for example, the item with the maximum value is D_(mins,S0) is determined. That is to say, when the item with the maximum value is D_(min,Sy), Sy is determined. By this means, the most probable bit within bit string (S0, S1, S2, S3) can be chosen. The above-described processing is summarized in FIG. 36.

First, when processing is started in step ST0, candidate signal point 3407 having the minimum Euclidian distance from reception point 3417 is detected in step ST1.

In step ST2, the bits contained in bit string (1, 1, 1, 1) corresponding to candidate signal point 3407 are inverted one bit at a time. In step ST3, for each inverted bit, a plurality of candidate signal points containing the inverted bit are searched for. In step ST4, for each inverted bit, the minimum Euclidian distance between a reception point and the plurality of candidate signal points found in step ST3 is detected. In step ST5, the maximum Euclidian distance is detected from among the minimum Euclidian distances of each inverted bit detected in step ST4. In step ST6, the bit corresponding to the maximum Euclidian distance detected in step ST5 is taken as the bit with the highest reliability within bit string (1, 1, 1, 1) represented by candidate signal point 3407 detected in step ST1, and this is adopted as a partial bit.

That is to say, in step ST2 through step ST6, the bit with the highest reliability within a bit string represented by a candidate signal point detected in step ST1 is determined. Then processing ends in step ST7.

Thus, according to this embodiment, 1 bit with an extremely low probability of being erroneous can be determined by: detecting a candidate signal point for which the Euclidian distance from a modulated signal reception point is a minimum; inverting the bits contained in the bit string corresponding to the detected candidate signal point one at a time; searching, for each inverted bit, for a plurality of candidate signal points containing the inverted bit; detecting, for each inverted bit, the minimum Euclidian distance between the reception point and the aforementioned found plurality of candidate signal points; detecting the maximum Euclidian distance among the minimum Euclidian distances of each aforementioned inverted bit; and determining the bit corresponding to the detected maximum Euclidian distance to be a partial bit.

If this kind of 1-bit determination algorithm is here executed by partial bit determination sections 509 and 512, a partial bit (1 bit) with an extremely low probability of being erroneous can be determined, enabling the bit error rate performance of a finally obtained received digital signal to be improved. The 1-bit determination algorithm of this embodiment is not limited to a case in which a receiving apparatus with a configuration described in an above embodiment is used, and can be widely applied to cases in which it is wished to select the bit with the lowest probability of being erroneous within a bit string represented by a signal point.

In this embodiment, 16QAM has been described as an example, but 1 bit can also be similarly determined when a different modulation method is used. Also, this embodiment can be similarly implemented when the squares of Euclidian distances are found instead of Euclidian distances.

Embodiment 9

In above Embodiment 3, a 64QAM partial bit determination method was described. In this embodiment, a 2-bit partial bit determination method and 4-bit partial bit determination method different from those described in Embodiment 3 will be described. Referring to FIG. 5, for example, the partial bit determination described below is performed by means of partial bit determination sections 509 and 512 with modulated signal A and B estimated baseband signals 508 and 511 separated by separation section 507 as reception points.

(i) 2-Bit Partial Bit Determination

FIG. 37 shows the relationship between signal points (candidate signal points) in a 64QAM in-phase I-orthogonal Q plane and the 6 bits transmitted at each signal point, and also the relationship of 2 partial bits determined by reception signal point presence positions. Specifically, in FIG. 37, the 6 bits shown under each signal point are the 6 bits corresponding to each signal point, and reference codes 3601 and 3602 denote reception points.

In this embodiment, the IQ plane is divided into 9 areas as indicated by the dotted lines. This area division method is a characteristic of this embodiment. With the area division shown in FIG. 37, the number of bits for which the determined bits are always the same in each area is two. That is to say, if six 64QAM bits are designated “first bit, second bit, third bit, fourth bit, fifth bit, sixth bit” sequentially from left to right, in the area in which reception point 3601 is present, third bit “0” and sixth bit “1” are the same for all signal points (candidate signal points). Also, in the area in which reception point 3602 is present, third bit “1” and fourth bit “1” are the same for all signal points (candidate signal points).

In this embodiment, which bits of the 6 bits making up one symbol are demodulated as partial bits is changed according to which of the divided areas a reception point is present in, while performing this kind of area division. In other words, when the IQ plane is divided into a plurality of areas, only bits with the same determined value in an area are demodulated as partial bits. By this means, partial bit error rate performance can be improved.

Specifically, when a reception point is present at the position indicated by reference code 3601, “xx0xx1” is determined. That is to say, only third bit “0” and sixth bit “1” are determined to be (demodulated as) partial bits. Here, x indicates indetermination (that is, a bit whose value is not determined).

Similarly, when a reception point is present at the position indicated by reference code 3602, “xx11xx” is determined. That is to say, only third bit “1” and fourth bit “1” are determined to be (demodulated as) partial bits. Incidentally, if a reception point is present on a boundary between areas, it may be assigned to either area.

Then candidate signal point reduction is performed based on the determined 2 partial bits, and the indeterminate 4 bits are found by likelihood detection.

(ii) 4-Bit Partial Bit Determination

Next, the 4-bit partial bit determination method will be explained using FIG. 38.

FIG. 38 shows the relationship between signal points (candidate signal points) in a 64QAM in-phase I-orthogonal Q plane and the 6 bits transmitted at each signal point, and also the relationship of 4 partial bits determined by reception signal point presence positions. Specifically, in FIG. 38, the 6 bits shown under each signal point are the 6 bits corresponding to each signal point, and reference codes 3701 and 3702 denote reception points.

In this embodiment, the IQ plane is divided into 49 areas as indicated by the dotted lines. With the area division shown in FIG. 38, the number of bits for which the determined bits are always the same in each area is four. That is to say, if six 64QAM bits are designated “first bit, second bit, third bit, fourth bit, fifth bit, sixth bit” sequentially from left to right, in the area in which reception point 3701 is present, second bit “1”, third bit “0”, fifth bit “1”, and sixth bit “0” are the same for all signal points (candidate signal points). Also, in the area in which reception point 3702 is present, second bit “1”, third bit “1”, fourth bit “1”, and sixth bit “0” are the same for all signal points (candidate signal points).

Here, when a reception point is present at the position indicated by reference code 3701, for example, “x10x10” is determined. That is to say, only second bit “1”, third bit “0”, fifth bit “1”, and sixth bit “0” are determined to be (demodulated as) partial bits.

Similarly, when a reception point is present at the position indicated by reference code 3702, “x111x0” is determined. That is to say, only second bit “1”, third bit “1”, fourth bit “1”, and sixth bit “0” are determined to be (demodulated as) partial bits.

Then candidate signal point reduction is performed based on the determined 4 partial bits, and the indeterminate 2 bits are found by likelihood detection.

Thus, according to this embodiment, in demodulating some bits of a modulated signal that has undergone 64QAM modulation, which bits in a 6-bit bit string making up one symbol are demodulated as partial bits is changed according to which area on the IQ plane a relevant reception signal point is present in, thereby improving the bit error performance of partial bits determined by partial bit determination sections 509 and 512, and so improving the reliability of reduced candidate signal points used by likelihood detection section 518. As a result, the bit error performance of final received digital signals 322 and 323 can be improved.

That is to say, if the kind of 2-bit or 4-bit determination algorithm described in this embodiment is executed by partial bit determination sections 509 and 512, partial bits (2 bits or 4 bits) with an extremely low probability of being erroneous can be determined, enabling the bit error rate performance of finally obtained received digital signals 322 and 323 to be improved. The 16QAM 2-bit or 4-bit determination algorithm of this embodiment is not limited to a case in which a receiving apparatus with a configuration described in an above embodiment is used, and can be widely applied to cases in which it is wished to select bits with the lowest probability of being erroneous within a bit string represented by a signal point.

In this embodiment, a method of determining 2 bits as partial bits and a method of determining 4 bits as partial bits have been described, and it is appropriate to select either of these methods based on the received field strength of a received signal. For example, 4-bit determination may be used when the received field strength of modulated signal A is greater than or equal to a predetermined threshold value, and 2-bit determination when the received field strength of modulated signal A is less than the threshold value. This enables the amount of computation to be reduced without lowering bit error rate performance.

Embodiment 10

In Embodiment 7, a method was described whereby the number of partial bit determinations is controlled according to the received field strength of each modulated signal. In this embodiment, a detailed description is given of the configuration of a receiving apparatus that finds the signal to noise ratio of each modulation method after inverse matrix computation or MMSE computation, and uses these to determine the number of partial bit determinations.

Assume that the vector (Rx1(t), Rx2(t), Rx3(t))T in Equation (2) is designated rx, the matrix in Equation (2) is designated H, and the vector (Txa(t), Txb(t), Txc(t)) T is designated tx. Then, if an added noise vector is designated n, Equation (2) can be represented as shown in the following equation. rx=Htx+n  (3)

When inverse matrix computation is performed, if the inverse matrix of H is represented by H⁻¹, the following equation is obtained from Equation (3). tx′=tx+H ⁻¹ n  (4)

where tx′ is a receiving apparatus estimate for tx.

Here, the signal to noise ratio after inverse matrix computation can be obtained by finding the ratio of tx signal power to noise power found from H⁻¹n. This is a known technology described, for example, in “A SDM-COFDM scheme employing a simple feed-forward inter-channel interference canceller for MIMO based broadband wireless LANs” IEICE Transaction on Communications, vol.E86-B, no. 1, pp. 283-290, January 2003, and therefore a detailed description thereof is omitted here.

Specifically, to give a description applicable to signal processing section 3117 in FIG. 34, for example, control section 3301 has modulated signal A channel fluctuation signals 308, 318, and 3112, modulated signal B channel fluctuation signals 310, 320, and 3114, and modulated signal C channel fluctuation signals 3102, 3104, and 3116 as input, finds H⁻¹ in Equation (4), and obtains the modulated signal A signal to noise ratio after inverse matrix computation, modulated signal B signal to noise ratio after inverse matrix computation, and modulated signal C signal to noise ratio after inverse matrix computation.

When the modulation method of modulated signals A, B, and C is 64QAM, and, for example, the relationship “modulated signal A signal to noise ratio after inverse matrix computation>modulated signal B signal to noise ratio after inverse matrix computation>modulated signal C signal to noise ratio after inverse matrix computation” holds true, and if the number of bits determined by modulated signal A partial bit determination section 509 is designated ma bits, the number of bits determined by modulated signal B partial bit determination section 512 is designated mb bits, and the number of bits determined by modulated signal C partial bit determination section 3208 is designated mc bits, control section 3301 controls the number of bits that are determined so that the relationship ma>mb>mc holds true. That is to say, more partial bit determinations are performed for a modulated signal with a larger signal to noise ratio after inverse matrix computation.

By controlling how many partial bits of each modulated signal are used in signal point reduction by signal point reduction sections 514, 516, and 3210 by means of control section 3301 based on the signal to noise ratio after inverse matrix computation of each modulated signal in this way, received digital signals 322, 323, and 3213 with significantly better bit error rate performance can be obtained.

When the modulation method is 64QAM, if the partial bit determination methods of Embodiment 8 or Embodiment 9 are used, 1 bit, 2 bits, and 4 bits are possible as number of bits ma, mb, and mc determined by the partial bit determination sections. However, this embodiment is not limited to this case, and if the signal to noise ratio after inverse matrix computation of a modulated signal is extremely large, all bits (that is, 6 bits) may be determined as partial bits.

A case has been described above in which the number of bits determined as partial bits is decided based on the signal to noise ratio after inverse matrix computation. Next, a case will be described in which the number of bits determined as partial bits is decided based on the signal to noise ratio after MMSE computation, which is a linear transformation similar to an inverse matrix computation.

Matrix G of the following equation is calculated based on matrix H in Equation (3). G=H ^(H)(HH ^(H)+σ² I)⁻¹  (5)

where H^(H) is the complex conjugate transpose of H, and I is a unit matrix.

An estimated signal of each modulated signal can be obtained by multiplying Equation (3) by the matrix of Equation (5). Then the signal to noise ratio of an estimated signal obtained by multiplying Equation (3) by the matrix of Equation (5) is calculated. Such signal to noise ratio calculation is a known technology described, for example, in “Performance improvement of ordered successive detection with imperfect channel estimates for MIMO systems” IEICE Transaction on Communications, vol.E86-B, no. 11, pp. 3200-3208, November 2003, and therefore a detailed description thereof is omitted here.

Specifically, to give a description applicable to signal processing section 3117 in FIG. 34, for example, control section 3301 has modulated signal A channel fluctuation signals 308, 318, and 3112, modulated signal B channel fluctuation signals 310, 320, and 3114, and modulated signal C channel fluctuation signals 3102, 3104, and 3116 as input, finds matrix G of Equation (5), multiplies Equation (3) by matrix G of Equation (5), and obtains the modulated signal A signal to noise ratio after MMSE computation, modulated signal B signal to noise ratio after MMSE computation, and modulated signal C signal to noise ratio after MMSE computation.

When the modulation method of modulated signals A, B, and C is 64QAM, and, for example, the relationship “modulated signal A signal to noise ratio after MMSE computation>modulated signal B signal to noise ratio after MMSE computation>modulated signal C signal to noise ratio after MMSE computation” holds true, and if the number of bits determined by modulated signal A partial bit determination section 509 is designated ma bits, the number of bits determined by modulated signal B partial bit determination section 512 is designated mb bits, and the number of bits determined by modulated signal C partial bit determination section 3208 is designated mc bits, control section 3301 controls the number of bits that are determined so that the relationship ma>mb>mc holds true. That is to say, more partial bit determinations are performed for a modulated signal with a larger signal to noise ratio after MMSE computation.

By controlling how many partial bits of each modulated signal are used in signal point reduction by signal point reduction sections 514, 516, and 3210 by means of control section 3301 based on the signal to noise ratio after MMSE computation of each modulated signal in this way, received digital signals 322, 323, and 3213 with significantly better bit error rate performance can be obtained.

In this embodiment, a case in which the number of transmitting antennas is 3, the number of receiving antennas is 3, and the number of transmit modulated signals is 3 has been described as an example, but this embodiment can be widely applied to cases with n transmitting antennas, n receiving antennas, and n transmit signals (where n>2). For example, in a case in which the number of transmitting antennas is 2, the number of receiving antennas is 2, and the number of transmit modulated signals is 2, if modulated signal A signal to noise ratio after inverse matrix computation or MMSE computation>modulated signal B signal to noise ratio after inverse matrix computation or MMSE computation, determination may be carried out whereby, for example, 4 partial bits are determined for modulated signal A, 2-bit or 1-bit partial determination is performed for modulated signal B, and the remaining bits are then included by performing likelihood determination.

As a result of performing a simulation, it was found that the method described in this embodiment, whereby partial bits used in candidate signal point reduction by signal point reduction sections are controlled according to the signal to noise ratio of a modulated signal after inverse matrix computation or MMSE computation, enables received digital signals 322, 323, and 3213 with extremely good bit error rate performances to be obtained especially when MMSE is performed by separation section 3201 (FIG. 34).

Embodiment 11

Generally, it is necessary for likelihood detection section 518 (3212) to find the square of the Euclidian distance between a candidate signal point and reception point, and the computational complexity (in particular, the number of multipliers) increases as the number of antennas and modulation M-ary number increase. The present invention reduces the computational complexity while suppressing degradation of bit error rate performance, and in this embodiment a method is proposed whereby the computational complexity of likelihood detection section 518 (3212) is significantly reduced compared with the above-described embodiments.

In this embodiment, calculation of Euclidian distance squares by likelihood detection section 518 (3212) is replaced by calculation for approximation by means of Manhattan distances. By this means, likelihood detection is performed by likelihood detection section 518 (3212) without using multipliers.

This calculation method will be explained using FIG. 39. The square of the Euclidian distance between a candidate signal point and reception signal point in the in-phase I-orthogonal Q plane, x²+y², is the value that it is actually wished to find. However, a method of approximating this as |x|+|y| is the Manhattan distance method. In the following description, |x|<|y| will be taken as an example, but when |x|>|y|, a similar procedure as for |x|<|y| can be assumed, with x and y switched around.

When a reception signal point is at position <1>, the Euclidian distance is 1.414x, whereas the Manhattan distance is 2x. Also, when a reception signal point is at position <2>, the Euclidian distance is x and the Manhattan distance is also x—that is, the Euclidian distance and Manhattan distance are equal. As can be seen from the above, as |x| increases (where |x|<|y|), the Manhattan distance approximation error relative to the Euclidian distance increases.

In this embodiment, a method of solving this problem is proposed. At this time, in this embodiment, the provision of multipliers is avoided, and an increase in computational complexity is prevented by using a configuration that employs a bit shift, adder, and comparator.

FIG. 40 shows the size relationship of |x| and |y|, and approximations of Euclidian distances found by likelihood detection according to this embodiment. Specifically, likelihood detection is performed with the Euclidian distance approximation taken to be |y| when the size relationship of I-direction distance x and Q-direction distance y for a candidate signal point and reception signal point on the IQ plane is 0≦|x|≦|y|×(¼+⅛), with the Euclidian distance approximation taken to be |y|×(1+⅛) when that size relationship is |y|×(¼+⅛)≦|x|≦|y|×(½+⅛), with the Euclidian distance approximation taken to be |y|×(1+¼) when that size relationship is, |y|×(½+⅛)≦|x|≦|y|×(½+¼+⅛), and with the Euclidian distance approximation taken to be |y|×(1+¼+⅛) when that size relationship is |y|×(½+¼+⅛)≦|x|. It is here assumed that |x|<|y|.

At this time, the multiplication factors are factors obtained by addition of any of 1, ½, ¼, or ⅛, and therefore all calculations can be composed of bit shifts and additions. Therefore, multipliers are not necessary, and an increase in computational complexity can be avoided. If |x|>|y|, FIG. 40 should be read with x and y switched around.

FIG. 41 shows a sample circuit configuration for implementing an approximation method by means of Manhattan distance as shown in FIG. 40. An |x| and |y| calculation section 4003 has candidate signal point information 4001 and reception signal point information 4002 as input, finds |x| and |y| in the in-phase I-orthogonal Q plane, and outputs these as 4004 and 4005. It is here assumed that |x|<|y|. That is to say, the larger of the two obtained absolute values is taken to be |y|, and the smaller is taken to be |x|.

A calculation section 4006 has |x| and |y| as input, finds a size relationship such as on the left side of FIG. 40 by means of a comparison operation, determines which of the four right-side expressions in FIG. 40 is to be used as a Euclidian distance approximation according to the comparison result, and finds a Euclidian distance approximation 4007 using the determined expression. Calculation section 4006 may, for example, be provided with a comparison operation section that performs the left-side comparison operations in FIG. 40 and four operation sections that implement the right-side expressions in FIG. 40, and may find Euclidian distance approximation 4007 by selecting an operation section corresponding to a comparison result among the four operation sections based on a comparison result obtained by the comparison operation section. In this case, the comparison operation section can perform operations for all the operation sections by means of bit shifts and additions only, enabling the kind of calculations in FIG. 40 to be implemented with low computational complexity.

By performing the above kind of approximation, a Euclidian distance approximation can be implemented with good precision and with low computational complexity.

With this embodiment, a case has been described in which a Euclidian distance approximation is found based on a correspondence table between size relationships and Euclidian approximations as shown in FIG. 40, but this embodiment is not limited to this approach, the essential point being that, as long as a Euclidian distance approximation is found by means of circuitry comprising a bit shift, adder, and comparator, a Euclidian distance approximation can be achieved with good precision and with low computational complexity.

Embodiment 12

Up to now, 1-bit and 2-bit partial bit determination methods have been described as 16QAM partial bit determination methods. In this embodiment, a 16QAM 3-bit partial bit determination method not hitherto dealt with will be described in detail.

FIG. 35 shows an example of 16QAM signal point arrangement and a received-signal signal point. In this figure, reference codes 3401 through 3416 denote 16QAM signal points (candidate signal points), and reference code 3417 denotes a received-signal signal point (reception point). FIG. 35 also shows the relationships of the 4 bits (S0, S1, S2, S3) of signal points 3401 through 3416.

In a 3-bit partial bit determination method of this embodiment, first, the Euclidian distances between received-signal signal point 3417 and 16QAM signal points 3401 through 3416 are found, the 16QAM signal point with the minimum Euclidian distance is found, and the 4 bits indicated by that signal point are found. In the example in FIG. 35, signal point 3407 is detected as the signal point having the minimum Euclidian distance from reception point 3417, and (S0, S1, S2, S3)=(1, 1, 1, 1) is found as the 4-bit bit string indicated by that signal point 3407.

Next, the following Euclidian distances are found for the 4 bits (S0, S1, S2, S3).

As “1” has been found for bit S0, signal points with “0” in the S0 position of bit string (S0, S1, S2, S3) are searched for. As a result of the search, signal points 3401, 3402, 3405, 3406, 3409, 3410, 3413, and 3414 are obtained. Then the minimum Euclidian distance between these 8 signal points and reception point 3417 is found, and the value of minimum Euclidian distance D_(min,S0) is found.

Similarly, as “1” has been found for bit S1, signal points with “0” in the S1 position of bit string (S0, S1, S2, S3) are searched for. As a result of the search, signal points 3401, 3404, 3405, 3408, 3409, 3412, 3413, and 3416 are obtained. Then the minimum Euclidian distance between these 8 signal points and reception point 3417 is found, and the value of minimum Euclidian distance D_(min,S1) is found.

Similarly, as “1” has been found for bit S2, signal points with “0” in the S2 position of bit string (S0, S1, S2, S3) are searched for. As a result of the search, signal points 3409, 3410, 3411, 3412, 3413, 3414, 3415, and 3416 are obtained. Then the minimum Euclidian distance between these 8 signal points and reception point 3417 is found, and the value of minimum Euclidian distance D_(min,S2) is found.

Similarly, as “1” has been found for bit S3, signal points with “0” in the S3 position of bit string (S0, S1, S2, S3) are searched for. As a result of the search, signal points 3401, 3402, 3403, 3404, 3413, 3414, 3415, and 3416 are obtained. Then the minimum Euclidian distance between these 8 signal points and reception point 3417 is found, and the value of minimum Euclidian distance D_(min,S3) is found.

That is to say, signal points that have a value that is the NOT of determined bit Sx are searched for, the minimum Euclidian distance between these signal points and reception point 3407 is found, and the value of minimum Euclidian distance D_(min,Sx) is found.

Then the item with the minimum value among D_(min,S0), D_(min,S1), D_(min,S2), and D_(min,S3) is searched for. If, for example, the item with the minimum value is D_(min,S0), the three bits other than S0—that is, is S1, S2, and S3—are determined. That is to say, when the item with the minimum value is D_(min,Sy), the bits other than Sy are determined. By this means, the most probable 3 bits within bit string (S0, S1, S2, S3) can be chosen.

The above-described processing is summarized in FIG. 42.

First, when processing is started in step ST0, candidate signal point 3407 having the minimum Euclidian distance from reception point 3417 is detected in step ST1.

In step ST2, the bits contained in bit string (1, 1, 1, 1) corresponding to candidate signal point 3407 are inverted one bit at a time. In step ST3, for each inverted bit, a plurality of candidate signal points containing the inverted bit are searched for. In step ST4, for each inverted bit, the minimum Euclidian distance between a reception point and the plurality of candidate signal points found in step ST3 is detected. In step ST5, the minimum Euclidian distance is detected from among the minimum Euclidian distances of each inverted bit detected in step ST4. In step ST6, the bit corresponding to the minimum Euclidian distance detected in step ST5 is taken to be the bit with the lowest reliability within bit string (1, 1, 1, 1) represented by candidate signal point 3407 detected in step ST1, and the value of bits other than this bit is determined.

That is to say, in step ST2 through step ST6, bits other than the bit with the lowest reliability within a bit string represented by a candidate signal point detected in step ST1 are determined. Then processing ends in step ST7.

Thus, according to this embodiment, 3 bits with an extremely low probability of being erroneous can be determined by: detecting a candidate signal point for which the Euclidian distance from a modulated signal reception point is a minimum; inverting the bits contained in the bit string corresponding to the detected candidate signal point one at a time; searching, for each inverted bit, for a plurality of candidate signal points containing the inverted bit; detecting, for each inverted bit, the minimum Euclidian distance between the reception point and the aforementioned found plurality of candidate signal points; detecting the minimum Euclidian distance among the minimum Euclidian distances of each aforementioned inverted bit; and determining bits other than the bit corresponding to the detected minimum Euclidian distance to be partial bits.

If this kind of 3-bit determination algorithm is here executed by partial bit determination sections 509 and 512, partial bits (3 bits) with an extremely low probability of being erroneous can be determined, enabling the bit error rate performance of a finally obtained received digital signal to be improved. The 3-bit determination algorithm of this embodiment is not limited to a case in which a receiving apparatus with a configuration described in an above embodiment is used, and can be widely applied to cases in which it is wished to select bits with a low probability of being erroneous within a bit string represented by a signal point.

In this embodiment, 16QAM has been described as an example, but bits excluding 1 bit can also be determined by means of the same kind of algorithm when a different modulation method is used. Also, this embodiment can be similarly implemented when the squares of Euclidian distances are found instead of Euclidian distances.

Embodiment 13

Up to now, a number of partial bit determination methods have been described for demodulating a plurality of modulated signals transmitted from a plurality of antennas with comparatively low computational complexity and with good bit error rate performance. This embodiment proposes the application of an above-described kind of partial bit determination method to MLD using QR decomposition, as shown, for example, in “Likelihood function for QR-MLD suitable for soft-decision turbo decoding and its performance for OFDM MIMO multiplexing in multipath fading channels,” IEICE Transaction on Communications vol.E88-B, no. 1, pp. 47-57, 2005.

FIG. 43 shows a sample configuration of this embodiment. In this embodiment, a case in which there are 3 transmitting antennas and 3 receiving antennas, and the modulation method is 16QAM, is described as an example. Signal processing section 4200 in FIG. 43 is used as signal processing section 3117 in FIG. 32.

Three modulated signals are transmitted from a transmitting apparatus, and when the receiving apparatus receives these modulated signals at three antennas, the relationship in Equation (2) holds true as described above. Here, the matrix in Equation (2) is assumed to be represented by H.

A QR decomposition section 4201 obtains triangular matrix R represented by the following equation by performing QR decomposition using unitary matrix Q.

$\begin{matrix} \begin{matrix} {R = {Q\; H}} \\ {= \begin{pmatrix} r_{11} & r_{12} & r_{13} \\ 0 & r_{22} & r_{23} \\ 0 & 0 & r_{33} \end{pmatrix}} \end{matrix} & (6) \end{matrix}$

Then QR decomposition section 4201 obtains the following relational expression by multiplying matrix Q complex conjugate transpose matrix Q^(H) by the Equation (2) received signals.

$\begin{matrix} {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q^{H}{Rx}} = {R\begin{pmatrix} {Tx}_{a} \\ {Tx}_{b} \\ {Tx}_{c} \end{pmatrix}}}} & (7) \end{matrix}$

QR decomposition section 4201 then outputs signal Z₁ (4202) obtained by means of Equation (7) to a candidate signal point computation section 4214, signal Z₂ (4203) to a candidate signal point computation section 4210, and signal Z₃ (4204) to a partial bit determination section 4208, and also outputs row 1 of matrix R (4205) obtained by means of Equation (6) to candidate signal point computation section 4214, row 2 of matrix R (4206) to candidate signal point computation section 4210, and row 3 of matrix R (4207) to partial bit determination section 4208.

Partial bit determination section 4208 has signal Z₃ (4204) and row 3 of matrix R (4207) as input. Here, signal Z₃ contains only a modulated signal Tx_(c) component. Therefore, 16QAM partial bit determination methods described hitherto can be used by performing channel fluctuation correction. Thus partial bit determination section 4208 outputs a high-likelihood partial bit 4209 of modulated signal Tx_(c) by performing the same kind of partial bit determination as in the above embodiments.

Candidate signal point computation section 4210 has signal Z₂ (4203), row 2 of matrix R (4206), and modulated signal Tx_(c) high-likelihood partial bit 4209 as input. Candidate signal point computation section 4210 performs signal point reduction using these, and outputs a candidate signal point signal 4211. This will now be explained in detail. Signal Z₂ is composed of only modulated signal TX_(b) and modulated signal Tx_(c) components. Therefore, when the signals are 16QAM signals, for example, there are 16 (modulated signal b)×16 (modulated signal c)=256 candidate signal points, but for modulated signal c, candidate signal point computation section 4210 computes candidate signal point signal 4211 using only 2 bits determined as having high likelihood by partial bit determination section 4208. That is to say, the number of candidate signal points computed by candidate signal point computation section 4210 is 16 (modulated signal b)×4 (modulated signal c)=64. In this way, candidate signal point computation section 4210 reduces the number of candidate signal points to be computed. In actuality, candidate signal point computation section 4210 finds branch metrics for candidate signal points reduced in this way, and outputs the results as candidate signal point signal 4211 to a candidate signal point selection section 4212.

Consequently, candidate signal point computation section 4210 performs branch metric computation only for a bit determined to have high likelihood by partial bit determination section 4208, reducing the amount of computation. For example, when the modulation method is 16 QAM in each case, MLD using conventional QR decomposition requires branch metrics to be computed by candidate signal point computation section 4210 for 16 (modulated signal b)×16 (modulated signal c)=256 points, whereas in this embodiment, when 2 bits are determined to be high-likelihood partial bits 4209 by partial bit determination section 4208, branch metrics need only be computed by candidate signal point computation section 4210 for 16 (modulated signal b)×4 (modulated signal c)=64 points.

As a result, computational complexity can be reduced. In addition, since partial bit determination section 4208 determines a high-likelihood partial bit 4209 accurately as in the above-described embodiments, and reduces candidate signal points on that basis, determination areas decrease. Consequently, both a reduction in computational complexity and an improvement in reception quality can be achieved.

Candidate signal point selection section 4212 has candidate signal point signal 4211 (comprising, for example, branch metrics of 64 candidate signal points) as input, selects therefrom a previously decided number of high-likelihood signal points (for example, 16 points) as candidate signal points, and outputs a candidate signal point signal 4213 indicating the selected candidate signal points. That is to say, candidate signal point selection section 4212 selects 16 high-likelihood points based on the branch metrics of 64 candidate signal points, for example, from candidate signal point computation section 4210, and outputs candidate signal point signal 4213 indicating those 16 points.

Candidate signal point computation section 4214 has signal Z₁ (4202), row 1 of matrix R (4205), and selected candidate signal point signal 4213 as input. Candidate signal point computation section 4214 performs signal point reduction using these, and outputs a candidate signal point signal 4215. This will now be explained in detail. Signal Z₁ is composed of modulated signal Tx_(a) and Tx_(b), and modulated signal Tx_(c), components. Therefore, when the signals are 16QAM signals, for example, there are 16 (modulated signal a)×16 (modulated signal b)×16 (modulated signal c)=4096 candidate signal points, but for modulated signal b and modulated signal c, candidate signal point computation section 4214 computes candidate signal point signal 4215 using only 4 bits selected by candidate signal point selection section 4212. That is to say, the number of candidate signal points computed by candidate signal point computation section 4214 is 16 (modulated signal a)×16 (modulated signals b, c)=256. In this way, candidate signal point computation section 4214 reduces the number of candidate signal points to be computed. In actuality, candidate signal point computation section 4214 finds branch metrics for candidate signal points reduced in this way, and outputs the results as candidate signal point signal 4215 to a candidate signal point decision section 4216.

Candidate signal point decision section 4216 finds the most probable candidate signal point from candidate signal point signal 4215 (comprising, for example, branch metrics of 256 candidate signal points), and outputs a candidate signal point signal 4217 indicating the most probable signal point. This candidate signal point signal 4217 corresponds, for example, to modulated signal A digital signal 322, modulated signal B digital signal 323, and modulated signal C digital signal 3118 in FIG. 33.

Thus, according to this embodiment, in performing MLD using QR decomposition, by determining a high-likelihood signal by performing partial bit determination for a QR decomposition signal (signal Z₁) containing only a single modulated signal component, and using that determination result in later-stage processing, computational complexity can be reduced without lowering bit error rate performance when performing MLD using QR decomposition.

In this embodiment, a case has been described in which the modulation method of each modulated signal is 16QAM, but this embodiment is not limited to this case, and the same kind of effect as in the above-described embodiment can also be obtained when the modulation method of each modulated signal is other than 16QAM. Also, a case has been described in which there are 3 transmitting antennas and 3 receiving antennas, but this embodiment is not limited to this case.

Embodiment 14

In this embodiment, a method is proposed that enables MLD using QR decomposition to be performed with a much simpler configuration than in Embodiment 13.

In this embodiment, a case is described by way of example in which a transmitting apparatus transmits different modulated signals A, B, and C from three antennas, and a receiving apparatus receives these at three antennas, in the same way as in Embodiment 13.

FIG. 44 shows a sample configuration of this embodiment. Signal processing section 4300 in FIG. 44 is used as signal processing section 3117 in FIG. 32. Signal 4301 in FIG. 44 indicates a signal group corresponding to signals 308, 310, 3102, 306, 318, 320, 3104, 316, 3112, 3114, 3116, and 3110 in FIG. 32.

QR decomposition sections 4302, 4304, and 4306 have signal group 4301 as input, and each perform different QR decomposition.

Specifically, QR decomposition section 4302 performs the transformation in Equation (8), QR decomposition section 4304 performs the transformation in Equation (9), and QR decomposition section 4304 performs the transformation in Equation (10).

$\begin{matrix} {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{X}^{H}{Rx}_{X}} = {R_{X}\begin{pmatrix} {Tx}_{c} \\ {Tx}_{a} \\ {Tx}_{b} \end{pmatrix}}}} & (8) \\ {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{Y}^{H}{Rx}_{Y}} = {R_{Y}\begin{pmatrix} {Tx}_{a} \\ {Tx}_{b} \\ {Tx}_{c} \end{pmatrix}}}} & (9) \\ {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{Z}^{H}{Rx}_{Z}} = {R_{Z}\begin{pmatrix} {Tx}_{b} \\ {Tx}_{c} \\ {Tx}_{a} \end{pmatrix}}}} & (10) \end{matrix}$

Here, Rx_(X)=(Tx_(c), Tx_(a), Tx_(b))^(T), Rx_(Y)=(Tx_(a), Tx_(b), Tx_(c))^(T), Rx_(Z)=(Tx_(b), Tx_(c), Tx_(a))^(T).

Then QR decomposition section 4302 outputs Equation (8) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4303; QR decomposition section 4304 outputs Equation (9) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4305; and QR decomposition section 4306 outputs Equation (10) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4307.

A bit unit branch metric computation section 4308 has signals 4303, 4305, and 4307 from QR decomposition sections 4302, 4304, and 4306 as input, and performs MLD for signals 4303, 4305, and 4307 by finding branch metrics in bit units for row 2 and row 3, excluding top row 1, in matrix R.

Specifically, bit unit branch metric computation section 4308 performs MLD for Tx_(a) and Tx_(b) by finding bit unit branch metrics based on row 2 and row 3 of Equation (8) using signal 4303. For example, assume that the modulation method of modulated signals A and B is QPSK. In this case, a branch metric is assumed to be expressed as B1 [a0] [a1] [b0] [b1] [c0] [c1]. Here, a0 and a1 mean 2 transmit bits of modulated signal A, and a0, a1=0 or 1. Similarly, b0 and b1 mean 2 transmit bits of modulated signal B, and b0, b1=0 or 1, while c0 and c1 mean 2 transmit bits of modulated signal C, and c0, c1=0 or 1. Bit unit branch metric computation section 4308 finding bit unit branch metrics based on row 2 and row 3 of matrix R shown in Equation (8) using signal 4303 is equivalent to finding branch metric B1 [a0] [a1] [b0] [b1] [X] [X], where X means indetermination. This is because a modulated signal C component is not included in row 2 or row 3 of Equation (8). Therefore, bit unit branch metric computation section 4308 finds a total of 16 branch metrics for modulated signals A and B using signal 4303.

Similarly, bit unit branch metric computation section 4308 performs MLD for Tx_(b) and Tx_(c) by finding bit unit branch metrics based on row 2 and row 3 of Equation (9) using signal 4305. Bit unit branch metric computation section 4308 finding bit unit branch metrics based on row 2 and row 3 of matrix R shown in Equation (9) using signal 4305 is equivalent to finding branch metric B2 [X] [X] [b0] [b1] [c0] [c1]. In this way, bit unit branch metric computation section 4308 finds a total of 16 branch metrics for modulated signals B and C using signal 4305. Similarly, bit unit branch metric computation section 4308 performs MLD for Tx_(c) and Tx_(a) by finding bit unit branch metrics based on row 2 and row 3 of Equation (10) using signal 4306. Bit unit branch metric computation section 4308 finding bit unit branch metrics based on row 2 and row 3 of matrix R shown in Equation (10) using signal 4305 is equivalent to finding branch metric B3 [a0] [a1] [X] [X] [c0] [c1]. In this way, bit unit branch metric computation section 4308 finds a total of 16 branch metrics for modulated signals C and A using signal 4307.

Next, bit unit branch metric computation section 4308 adds the branch metrics obtained as described above on a bit-by-bit basis. Assuming that a branch metric is designated Ba0,0 when bit a0 of modulated signal A is “0”, for example, branch metric Ba0,0 is found as follows.

$\begin{matrix} {{{Ba}\; 0},{0 = {{B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (11) \end{matrix}$

Assuming that a branch metric is designated Ba0,1 when bit a0 of modulated signal A is “1”, bit unit branch metric computation section 4308 finds branch metric Ba0,1 as follows.

$\begin{matrix} {{{Ba}\; 0},{1 = {{B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (12) \end{matrix}$

Bit unit branch metric computation section 4308 finds branch metrics Ba1,0 and Ba1,1 when bit a1 of modulated signal A is “0” and “1” in a similar way.

Assuming that a branch metric is designated Bb0,0 when bit b0 of modulated signal B is “0”, bit unit branch metric computation section 4308 finds branch metric Bb0,0 as follows.

$\begin{matrix} {{{Bb}\; 0},{0 = {{B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (13) \end{matrix}$

Assuming that a branch metric is designated Bb0,1 when bit b0 of modulated signal B is “1”, bit unit branch metric computation section 4308 finds branch metric Bb0,1 as follows.

$\begin{matrix} {{{Bb}\; 0},{1 = {{B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (14) \end{matrix}$

Bit unit branch metric computation section 4308 finds branch metrics Bb1,0 and Bb1,1 when bit b1 of modulated signal B is “0” and “1” in a similar way.

Assuming that a branch metric is designated Bc0,0 when bit c0 of modulated signal C is “0”, bit unit branch metric computation section 4308 finds branch metric Bc0,0 as follows.

$\begin{matrix} {{{Bc}\; 0},{0 = {{B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}}}}} & (15) \end{matrix}$

Assuming that a branch metric is designated Bc0,1 when bit c0 of modulated signal C is “1”, bit unit branch metric computation section 4308 finds branch metric Bc0,1 as follows.

$\begin{matrix} {{{Bc}\; 0},{1 = {{B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (15) \end{matrix}$

Bit unit branch metric computation section 4308 finds branch metrics Bc1,0 and Bc1,1 when bit c1 of modulated signal C is “0” and “1” in a similar way.

Then bit unit branch metric computation section 4308 outputs the values obtained as described above as a modulated signal A bit unit branch metric group signal 4309, a modulated signal B bit unit branch metric group signal 4310, and a modulated signal C bit unit branch metric group signal 4311.

A determination section 4312 determines the most probable signal point for modulated signals A, B, and C based on modulated signal A bit unit branch metric group signal 4309, modulated signal B bit unit branch metric group signal 4310, and modulated signal C bit unit branch metric group signal 4311, and outputs the determination result as receive data 4313. This receive data 4313 corresponds, for example, to modulated signal A digital signal 322, modulated signal B digital signal 323, and modulated signal C digital signal 3118 in FIG. 33.

Thus, according to this embodiment, by providing a plurality of QR decomposition sections 4302, 4304, and 4306 that perform different QR decomposition, a bit unit branch metric computation section 4308 that finds branch metrics for signals 4303, 4305, and 4307 obtained by QR decomposition sections 4302, 4304, and 4306 based on rows other than the top row (in the example in this embodiment, row 2 and row 3 of matrix R, excluding row 1), and a determination section 4312 that performs likelihood determination based on those branch metrics, computational complexity can be reduced without lowering bit error rate performance when performing MLD using QR decomposition.

As compared with a configuration that narrows down candidate signal points in stages, such as shown in FIG. 43, for example, the fact that a configuration in which candidate signal points are passed on is not necessary enables computational complexity to be simplified and also reduces delay due to computation, making high-speed operation possible.

Differences in the design concept of MLD that omits the top row in QR decomposition according to this embodiment, and conventional QR-MLD, will now be mentioned. In a system with 3 transmitting antennas and 3 receiving antennas, for example, conventional QR-MLD provides an MLD approximation algorithm for obtaining diversity gain of the 3 receiving antennas. On the other hand, this embodiment can be said to provide an MLD approximation algorithm for obtaining diversity of 2 receiving antennas. That is to say, generally speaking, in a system with M transmitting antennas and M receiving antennas, conventional QR-MLD provides an MLD approximation algorithm for obtaining diversity gain of M receiving antennas, whereas this embodiment provides an MLD approximation algorithm for obtaining diversity of M-P receiving antennas (where M>P).

A characteristic of this embodiment is that, as described above, computational complexity can be reduced compared with conventional QR-MLD. A further characteristic is that, when above value M is large, a major difference in reception quality compared with that of conventional QR-MLD does not occur as long as P is set to a low value.

Incidentally, MMSE extension can also be implemented in a similar way as an MLD method using QR decomposition. This is a known technology mentioned, for example, in “Investigation of QRM-MLD Performing MMSE Extension in a Single-User/Multi-User MIMO Transmission Method” IEICE Technical Report RCS2005-190, March 2006, pp. 73-78, and therefore a description thereof is omitted here.

With this embodiment, computational complexity can be further significantly reduced by adding a configuration that executes partial bit determination on the bottom row in the same way as in Embodiment 13.

In this embodiment, a case has been described by way of example in which the number of modulated signals is 3, but this embodiment is not limited to this case, and can also be implemented in the same way when there are 4 or more modulated signals. For example, this embodiment can also be applied to a case in which a transmitting apparatus transmits different modulated signals from 4 antennas. In this case, whereas MLD was performed on row 2 and row 3 after QR decomposition in the above-described embodiment, MLD may be executed on row 3 and row 4 after QR decomposition, or MLD may be executed on row 2, row 3, and row 4 after QR decomposition. That is to say, MLD should be performed based on rows other than the top row(s) after QR decomposition.

In this embodiment, a case has been described in which the modulation method of each modulated signal is QPSK, but this embodiment is not limited to this case.

The method of finding branch metrics is not limited to an adding method such as described above. For example, branch metric Ba0,0 for a case in which bit a0 of modulated signal A is “0” may be taken as the minimum value among the following: B1 [0] [0] [0] [0] [X] [X], B1 [0] [0] [0] [1] [X] [X], B1 [0] [0] [1] [0] [X] [X], B1 [0] [0] [1] [1] [X] [X], B1 [0] [1] [0] [0] [X] [X], B1 [0] [1] [0] [1] [X] [X], B1 [0] [1] [1] [0] [X] [X], B1 [0] [1] [1] [1] [X] [X], B3 [0] [0] [X] [X] [0] [0], B3 [0] [0] [X] [X] [0] [1], B3 [0] [0] [X] [X] [1] [0], B3 [0] [0] [X] [X] [1] [1], B3 [0] [1] [X] [X] [0] [0], B3 [0] [1] [X] [X] [0] [1], B3 [0] [1] [X] [X] [1] [0], B3 [0] [1] [X] [X] [1] [1].

A branch metric found in this embodiment corresponds to a posterior probability when decoded. The use of prior probabilities will enable reception quality to be significantly improved. In order to use prior probabilities in this embodiment, it is necessary to find the inverse matrix of the matrix formed by row 2 and row 3 in Equation (8), Equation (9), and Equation (10), for example, find the SNR after separation from that inverse matrix (see above Equation (3) and Equation (4)), and use this.

Embodiment 15

In this embodiment, a configuration and method are proposed that enable computational complexity to be reduced without lowering bit error rate performance when performing MLD using QR decomposition by providing a plurality of QR decomposition sections that perform different QR decomposition in basically the same way as in Embodiment 14. This embodiment differs from Embodiment 14 with regard to the nature of the plurality of QR decompositions.

In this embodiment, a case is described by way of example in which a transmitting apparatus transmits different modulated signals A, B, and C from three antennas, and a receiving apparatus receives these at three antennas, in the same way as in Embodiment 14.

FIG. 45 shows a sample configuration of this embodiment. Signal processing section 4400 in FIG. 45 is used as signal processing section 3117 in FIG. 32. Signal 4301 in FIG. 45 indicates a signal group corresponding to signals 308, 310, 3102, 306, 318; 320, 3104, 316, 3112, 3114, 3116, and 3110 in FIG. 32.

QR decomposition sections 4302, 4304, and 4306 have signal group 4301 as input, and each perform different QR decomposition.

Specifically, QR decomposition section 4401A performs the transformation in Equation (17), QR decomposition section 4402A performs the transformation in Equation (18), QR decomposition section 4401B performs the transformation in Equation (19), QR decomposition section 4402B performs the transformation in Equation (20), QR decomposition section 4401C performs the transformation in Equation (21), and QR decomposition section 4402C performs the transformation in Equation (22).

$\begin{matrix} {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{a\; 1}^{H}{Rx}_{a\; 1}} = {R_{a\; 1}\begin{pmatrix} {Tx}_{c} \\ {Tx}_{b} \\ {Tx}_{a} \end{pmatrix}}}} & (17) \\ {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{a\; 2}^{H}{Rx}_{a\; 2}} = {R_{a\; 2}\begin{pmatrix} {Tx}_{b} \\ {Tx}_{c} \\ {Tx}_{a} \end{pmatrix}}}} & (18) \\ {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{b\; 1}^{H}{Rx}_{b\; 1}} = {R_{b\; 1}\begin{pmatrix} {Tx}_{c} \\ {Tx}_{a} \\ {Tx}_{b} \end{pmatrix}}}} & (19) \\ {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{b\; 2}^{H}{Rx}_{b\; 2}} = {R_{b\; 2}\begin{pmatrix} {Tx}_{a} \\ {Tx}_{c} \\ {Tx}_{b} \end{pmatrix}}}} & (20) \\ {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{c\; 1}^{H}{Rx}_{c\; 1}} = {R_{c\; 1}\begin{pmatrix} {Tx}_{b} \\ {Tx}_{a} \\ {Tx}_{c} \end{pmatrix}}}} & (21) \\ {\begin{pmatrix} Z_{1} \\ Z_{2} \\ Z_{3} \end{pmatrix} = {{Q_{c\; 2}^{H}{Rx}_{c\; 2}} = {R_{c\; 2}\begin{pmatrix} {Tx}_{a} \\ {Tx}_{b} \\ {Tx}_{c} \end{pmatrix}}}} & (22) \end{matrix}$

Here, Rx_(a1)=(Tx_(c), Tx_(b), Tx_(a))^(T), Rx_(a2)=(T x_(b), Tx_(c), Tx_(a))^(T), Rx_(b1)=(Tx_(c), Tx_(a), Tx_(b))^(T), Rx_(b2)=(Tx_(a), Tx_(c), Tx_(b))^(T), Rx_(c1)=(Tx_(a), Tx_(b), Tx_(c)) ^(T), Rx_(c2)=(Tx_(a), Tx_(b), Tx_(c))^(T).

Then QR decomposition section 4401A outputs Equation (17) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4403A; QR decomposition section 4402A outputs Equation (18) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4404A; QR decomposition section 4401B outputs Equation (19) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4403B; QR decomposition section 4402B outputs Equation (20) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4404B; QR decomposition section 4401C outputs Equation (21) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4403C; and QR decomposition section 4402C outputs Equation (22) signal Z₁, signal Z₂, signal Z₃, row 1 of matrix R, row 2 of matrix R, and row 3 of matrix R as signal 4404C.

A bit unit branch metric computation section 4405A has signals 4403A and 4404A from QR decomposition sections 4401A and 4402A as input, and performs MLD for signals 4403A and 4404A by finding branch metrics in bit units for row 2 and row 3, excluding top row 1, in matrix R.

Specifically, bit unit branch metric computation section 4405A performs MLD for Tx_(a) and Tx_(b) by finding bit unit branch metrics based on row 2 and row 3 of Equation (17) using signal 4403A. Also, bit unit branch metric computation section 4405A performs MLD for Tx_(a) and Tx_(c) by finding bit unit branch metrics based on row 2 and row 3 of Equation (18) using signal 4404A. For example, when the modulation method of each modulated signal is QPSK, bit unit branch metric computation section 4405A finds bit unit branch metric B1 [a0] [a1] [b0] [b1] [X] [X] based on row 2 and row 3 of matrix R shown in Equation (17) using signal 4403A. That is to say, bit unit branch metric computation section 4405A finds a total of 16 branch metrics for modulated signals A and B using signal 4403A. Also, bit unit branch metric computation section 4405A finds bit unit branch metric B2 [a0] [a1] [X] [X] [c0] [c1] based on row 2 and row 3 of matrix R shown in Equation (18) using signal 4404A. That is to say, bit unit branch metric computation section 4405A finds a total of 16 branch metrics for modulated signals A and C using signal 4404A.

Next, bit unit branch metric computation section 4405A adds the branch metrics obtained as described above on a bit-by-bit basis. Assuming that a branch metric is designated Ba0,0 when bit a0 of modulated signal A is “0”, for example, branch metric Ba0,0 is found as follows.

$\begin{matrix} {{{Ba}\; 0},{0 = {{B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (23) \end{matrix}$

Assuming that a branch metric is designated Ba0,1 when bit a0 of modulated signal A is “1”, bit unit branch metric computation section 4405A finds branch metric Ba0,1 as follows.

$\begin{matrix} {{{Ba}\; 0},{1 = {{B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{1\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{2\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{2\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{2\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (24) \end{matrix}$

Bit unit branch metric computation section 4405A finds branch metrics Ba1,0 and Ba1,1 when bit a1 of modulated signal A is “0” and “1” in a similar way, and then outputs the values obtained as described above as a modulated signal A bit unit branch metric group signal 4406A.

A bit unit branch metric computation section 4405B has signals 4403B and 4404B from QR decomposition sections 4401B and 4402B as input, and performs MLD for signals 4403B and 4404B by finding branch metrics in bit units for row 2 and row 3, excluding top row 1, in matrix R.

Specifically, bit unit branch metric computation section 4405B performs MLD for Tx_(b) and Tx_(a) by finding bit unit branch metrics based on row 2 and row 3 of Equation (19) using signal 4403B. Also, bit unit branch metric computation section 4405B performs MLD for Tx_(b) and Tx_(c) by finding bit unit branch metrics based on row 2 and row 3 of Equation (20) using signal 4404B. For example, when the modulation method of each modulated signal is QPSK, bit unit branch metric computation section 4405B finds bit unit branch metric B3 [a0] [a1] [b0] [b1] [X] [X] based on row 2 and row 3 of matrix R shown in Equation (19) using signal 4403B. That is to say, bit unit branch metric computation section 4405B finds a total of 16 branch metrics for modulated signals B and A using signal 4403B. Also, bit unit branch metric computation section 4405B finds bit unit branch metric B4 [X] [X] [b0] [b1] [c0] [c1] based on row 2 and row 3 of matrix R shown in Equation (20) using signal 4404B. That is to say, bit unit branch metric computation section 4405B finds a total of 16 branch metrics for modulated signals B and C using signal 4404B.

Next, bit unit branch metric computation section 4405B adds the branch metrics obtained as described above on a bit-by-bit basis. Assuming that a branch metric is designated Bb0,0 when bit b0 of modulated signal B is “0”, for example, branch metric Bb0,0 is found as follows.

$\begin{matrix} {{{Bb}\; 0},{0 = {{B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (25) \end{matrix}$

Assuming that a branch metric is designated Bb0,1 when bit b0 of modulated signal B is “1”, bit unit branch metric computation section 4405B finds branch metric Bb0,1 as follows.

$\begin{matrix} {{{Bb}\; 0},{1 = {{B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{3\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{4\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (26) \end{matrix}$

Bit unit branch metric computation section 4405B finds branch metrics Bb1,0 and Bb1,1 when bit b1 of modulated signal B is “0” and “1” in a similar way, and then outputs the values obtained as described above as a modulated signal B bit unit branch metric group signal 4406B.

A bit unit branch metric computation section 4405C has signals 4403C and 4404C from QR decomposition sections 4401C and 4402C as input, and performs MLD for signals 4403C and 4404C by finding branch metrics in bit units for row 2 and row 3, excluding top row 1, in matrix R.

Specifically, bit unit branch metric computation section 4405C performs MLD for Tx_(c) and Tx_(a) by finding bit unit branch metrics based on row 2 and row 3 of Equation (21) using signal 4403C. Also, bit unit branch metric computation section 4405C performs MLD for Tx_(c) and Tx_(b) by finding bit unit branch metrics based on row 2 and row 3 of Equation (22) using signal 4404C. For example, when the modulation method of each modulated signal is QPSK, bit unit branch metric computation section 4405C finds bit unit branch metric B3 [a0] [a1] [X] [X] [c0] [c1] based on row 2 and row 3 of matrix R shown in Equation (21) using signal 4403C. That is to say, bit unit branch metric computation section 4405C finds a total of 16 branch metrics for modulated signals C and A using signal 4403C. Also, bit unit branch metric computation section 4405C finds bit unit branch metric B6 [X] [X] [b0] [b1] [c0] [c1] based on row 2 and row 3 of matrix R shown in Equation (22) using signal 4404C. That is to say, bit unit branch metric computation section 4405C finds a total of 16 branch metrics for modulated signals C and B using signal 4404C.

Next, bit unit branch metric computation section 4405C adds the branch metrics obtained as described above on a bit-by-bit basis. Assuming that a branch metric is designated Bc0,0 when bit c0 of modulated signal C is “0”, for example, branch metric Bc0,0 is found as follows.

$\begin{matrix} {{{Bc}\; 0},{0 = {{B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{5\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{5\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{5\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{5\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{5\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{5\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{5\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{5\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}}}}} & (27) \end{matrix}$

Assuming that a branch metric is designated Bc0,1 when bit c0 of modulated signal C is “1”, bit unit branch metric computation section 4405C finds branch metric Bc0,1 as follows.

$\begin{matrix} {{{Bc}\; 0},{1 = {{B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{6\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{5\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{5\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{5\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{5\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 0\rbrack}} + {B\;{{{{{{5\lbrack 0\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{5\lbrack 0\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{5\lbrack 1\rbrack}\lbrack 0\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}} + {B\;{{{{{{5\lbrack 1\rbrack}\lbrack 1\rbrack}\lbrack X\rbrack}\lbrack X\rbrack}\lbrack 1\rbrack}\lbrack 1\rbrack}}}}} & (28) \end{matrix}$

Bit unit branch metric computation section 4405C finds branch metrics Bc1,0 and Bc1,1 when bit c1 of modulated signal C is “0” and “1” in a similar way, and then outputs the values obtained as described above as a modulated signal C bit unit branch metric group signal 4406C.

A determination section 4407 determines the most probable signal point for modulated signals A, B, and C based on modulated signal A bit unit branch metric group signal 4406A, modulated signal B bit unit branch metric group signal 4406B, and modulated signal C bit unit branch metric group signal 4406C, and outputs the determination result as receive data 4408. This receive data 4408 corresponds, for example, to modulated signal A digital signal 322, modulated signal B digital signal 323, and modulated signal C digital signal 3118 in FIG. 33.

Comparing the configuration of Embodiment 14 with the configuration of this embodiment, in Embodiment 14 QR decomposition is performed by switching all rows among QR decomposition sections 4302, 4304, and 4306, whereas in this embodiment QR decomposition is performed by keeping the bottom row (row 3) fixed and switching the other rows between QR decomposition sections 4401A and 4402A, between QR decomposition sections 4401B and 4402B, and between QR decomposition sections 4401C and 4402C.

Thus, according to this embodiment, by providing a plurality of QR decomposition sections 4401A, 4402A, 4401B, 4402B, 4401C, and 4402C that perform different QR decomposition, bit unit branch metric computation sections 4405A, 4405B, and 4405C that find branch metrics for signals 4403A, 4404A, 4403B, 4404B, 4403C, and 4404C obtained by QR decomposition sections 4401A, 4402A, 4401B, 4402B, 4401C, and 4402C based on rows other than the top row (in the example in this embodiment, row 2 and row 3 of matrix R, excluding row 1), and a determination section 4407 that performs likelihood determination based on those branch metrics, computational complexity can be reduced without lowering bit error rate performance when performing MLD using QR decomposition.

As compared with a configuration that narrows down candidate signal points in stages, such as shown in FIG. 43, for example, the fact that a configuration in which candidate signal points are passed on is not necessary enables computational complexity to be simplified and also reduces delay due to computation, making high-speed operation possible.

In this embodiment, a case has been described by way of example in which the number of modulated signals is 3, but this embodiment is not limited to this case, and can also be implemented in the same way when there are 4 or more modulated signals. With 3 modulated signals, MLD is performed for row 2 and row 3 after QR decomposition, and QR decomposition is performed so that a modulated signal to be found belongs to the bottom row, row 3, but when, for example, a transmitting apparatus transmits different modulated signals from four antennas, MLD can be executed for row 3 and row 4 after QR decomposition, and QR decomposition performed so that a modulated signal to be found belongs to the bottom row, row 4. In this case, for example, MLD can be performed for row 2, row 3, and row 4 after QR decomposition, and QR decomposition performed so that a modulated signal to be found belongs to the bottom row, row 4.

In this embodiment, a case has been described in which the modulation method of each modulated signal is QPSK, but this embodiment is not limited to this case.

The method of finding branch metrics is not limited to an adding method such as described above. For example, branch metric Ba0,0 for a case in which bit a0 of modulated signal A is “0” may be taken as the minimum value among the following: B1 [0] [0] [0] [0] [X] [X], B1 [0] [0] [0] [1] [X] [X], B1 [0] [0] [1] [0] [X] [X], B1 [0] [0] [1] [1] [X] [X], B1 [0] [1] [0] [0] [X] [X], B1 [0] [1] [0] [1] [X] [X], B1 [0] [1] [1] [0] [X] [X], B1 [0] [1] [1] [1] [X] [X], B2 [0] [0] [X] [X] [0] [0], B2 [0] [0] [X] [X] [0] [1], B2 [0] [0] [X] [X] [1] [0], B2 [0] [0] [X] [X] [1] [1], B2 [0] [1] [X] [X] [0] [0], B2 [0] [1] [X] [X] [0] [1], B2 [0] [1] [X] [X] [1] [0], B2 [0] [1] [X] [X] [1] [1].

A branch metric found in this embodiment corresponds to a posterior probability when decoded. The use of prior probabilities will enable reception quality to be significantly improved. In order to use prior probabilities in this embodiment, it is necessary to find the inverse matrix of the matrix formed by row 2 and row 3 in Equation (18), Equation (19), Equation (20), Equation (21), and Equation (22), for example, find the SNR after separation from that inverse matrix (see above Equation (3) and Equation (4)), and use this.

In this embodiment a case has been described in which QR decomposition is performed for all combinations in which each modulated signal is fixed in the bottom row and the other rows are switched around, and branch metrics are found, but it is not absolutely for QR decomposition and branch metric computation to be performed for all combinations in which each modulated signal is the bottom row. For example, in this embodiment, to consider modulated signal A, QR decomposition is performed for all cases in which modulated signal A is the bottom row—that is, for Equation (17) and Equation (18). However, a modulated signal A branch metric may be found with Equation (17) only, enabling the computational complexity to be reduced. In particular, the number of times QR decomposition is performed when the number of transmit modulated signals increases leads to a sharp increase in computational complexity, and therefore setting the number of QR decomposition processing operations as appropriate is effective from the standpoint of reducing computational complexity. The computational complexity can be effectively reduced if, for example, the number of QR decomposition processing operations is increased for a more important modulated signal, and decreased for a less important modulated signal.

Other Embodiments

In the above embodiments, cases have mainly been described, by way of example, in which the present invention is applied to spread spectrum communication scheme and OFDM scheme. But the present invention is not limited to these cases, and similar effects can also be obtained when a single-carrier system or a multicarrier system other than OFDM, or a system combining use of a multicarrier system and spread spectrum communication scheme with MIMO transmission applied therein, is used.

Also, although cases in which modulation which has 16 signal points is used as the modulation method have mainly been described, similar effects can also be obtained when M-ary modulation other than modulation which has 16 signal points is used. That is to say, in the above embodiments, partial bits have been found as shown in FIG. 9B, FIG. 11B, and FIG. 15B when a modulation signal which has 16 signal points is received, but this is not a limitation. The same kind of effects as in the above-described embodiments can be obtained when, in the case of an m-value modulation method that transmits m bits in 1 symbol, for example, m bits are reduced to m-k bits based on k (k<m) bits found by means of partial bit determination (that is, the number of candidate signal points is reduced), and likelihood detection is performed for the reduced candidate signal points. Furthermore, the area division method used when finding partial bits is not limited to the method in FIG. 9B, FIG. 11B, FIG. 15B, FIG. 17, FIG. 18, or FIG. 19, and a different division method can be applied.

In the above embodiments, cases have mainly been described in which inverse matrix computations are performed in determining partial bits, but the partial bit determination method is not limited to this, and, essentially, the same kind of effects as in the above-described embodiments can be obtained as long as partial bits are found by means of a detection method different from likelihood detection and a detection method involving a smaller amount of computation than likelihood decoding, since the amount of computation can be reduced compared with a case in which all bits are found by means of likelihood detection.

Furthermore, in the above embodiments, a case has generally been described, by way of example, in which the number of transmitting antennas is 2, the number of receiving antennas is 2, and the number of transmit modulated signals is 2, but the present invention is not limited to this case, and can also be applied to an apparatus with n transmitting antennas, n receiving antennas, and n transmit signals (where n≧3). Moreover, the present invention can also be applied to an apparatus aimed at improving the degree of separation and/or reception quality by using more receiving antennas than transmitting antennas and transmit signals, and performing combining or selection diversity when performing separation and signal point reduction.

The present invention is not limited to the above-described embodiments, and various variations and modifications may be possible without departing from the scope of the present invention.

According to one aspect of a receiving apparatus of the present invention, a receiving apparatus that receives modulated signals transmitted from a transmitting apparatus that transmits different modulated signals from a plurality of antennas employs a configuration that includes: a channel fluctuation estimation section that finds a channel estimate of each modulated signal; a partial bit demodulation section that demodulates only some bits of a modulated signal using a detection method different from likelihood detection; a signal point reduction section that reduces the number of candidate signal points using demodulated partial bits and a channel estimate; and a likelihood detection section that performs likelihood detection using a reduced number of candidate signal points and a received baseband signal.

According to this configuration, since demodulation of only some bits is performed by the partial bit demodulation section using a detection method different from likelihood detection, partial bits can be obtained with a small amount of computation. Also, since likelihood detection is performed by the likelihood detection section using a reduced number of candidate signal points, the remaining bits can be found with a high degree of precision using a small amount of computation. As likelihood detection is performed on a partial basis in this way, received digital signals with good bit error rate performances can be obtained while reducing the number of computations for finding Euclidian distances.

According to one aspect of a receiving apparatus of the present invention, a configuration is employed that further includes a control section that controls which modulated signals' partial bits are used for candidate signal point reduction by a signal point reduction section based on the reception quality of each modulated signal.

According to this configuration, compared with a case in which signal point reduction is performed by simply using partial bits of all modulated signals, it is possible to provide for partial bits with a high probability of being erroneous not to be used in signal point reduction processing, enabling more accurate signal point reduction processing to be performed, and received digital signals with significantly better bit error rate performances to be obtained.

According to one aspect of a receiving apparatus of the present invention, a configuration is employed that further includes a control section that controls how many partial bits of each modulated signal are used for candidate signal point reduction by a signal point reduction section based on the reception quality of each modulated signal.

According to this configuration, it is possible to provide for partial bits with a high probability of being erroneous not to be used in signal point reduction processing, enabling more accurate signal point reduction processing to be performed, and received digital signals with significantly better bit error rate performances to be obtained, compared with a case in which signal point reduction is performed by simply using the same number of partial bits for all modulated signals.

According to one aspect of a receiving apparatus of the present invention, a partial bit demodulation section employs a configuration that includes: a separation section that separates a received signal into modulated signals; and a partial bit determination section that finds a candidate signal point for which the Euclidian distance from the separated modulated signal reception point is a minimum, inverts the bits contained in the bit string corresponding to the found candidate signal point one at a time, searches, for each inverted bit, for a plurality of candidate signal points containing the inverted bit, detects, for each inverted bit, the minimum Euclidian distance between the reception point and the aforementioned plurality of candidate signal points, detects the maximum Euclidian distance among the minimum Euclidian distances of each aforementioned inverted bit, and determines 1 bit corresponding to the detected maximum Euclidian distance to be a demodulation partial bit.

According to this configuration, 1 bit with an extremely low probability of being erroneous can be obtained by the partial bit determination section, enabling more accurate signal point reduction processing to be performed, and received digital signals with significantly better bit error rate performances to be obtained.

According to one aspect of a receiving apparatus of the present invention, a partial bit demodulation section employs a configuration that includes: a separation section that separates modulated signals by performing inverse matrix computation on a channel estimation matrix using a channel estimate; and a partial bit determination section that determines partial bits of a separated modulated signal.

According to one aspect of a receiving apparatus of the present invention, a partial bit determination section employs a configuration that includes: a separation section that separates modulated signals by performing MMSE (Minimum Mean Square Error) computation on a channel estimation matrix using a channel estimate; and a partial bit determination section that determines partial bits of separated modulated signals.

According to these configurations, partial bits can be determined using a small amount of computation compared with a case of likelihood detection.

One aspect of a partial bit determination method of the present invention includes: a minimum distance candidate point detecting step of detecting a candidate signal point for which the Euclidian distance from a modulated signal reception point is a minimum; an inverting step of inverting the bits contained in the bit string corresponding to the detected candidate signal point one at a time; a step of searching, for each inverted bit, for a plurality of candidate signal points containing the inverted bit; a step of detecting, for each inverted bit, the minimum Euclidian distance between the reception point and the aforementioned found plurality of candidate signal points; a step of detecting the maximum Euclidian distance among the minimum Euclidian distances of each inverted bit; and a step of determining the bit corresponding to the detected maximum Euclidian distance to be a partial bit.

According to this method, the bit with the highest reliability can be determined within a bit string represented by a candidate signal point detected in the minimum distance candidate point detecting step, enabling 1 bit with an extremely low probability of being erroneous to be determined.

According to one aspect of a transmitting apparatus of the present invention, a transmitting apparatus that transmits different modulated signals from a plurality of antennas employs a configuration that includes: a modulation section that obtains a modulated signal by performing signal point mapping of transmit bits using a signal point arrangement that is divided into a plurality of signal point sets on the IQ plane, and whereby the minimum distance between signal points within a signal point set is smaller than the minimum signal point distance between signal point sets; and an antenna that transmits a modulated signal obtained by the modulation section.

According to this configuration, a bit common to signal points within a signal set can be determined easily and accurately on the receiving side. Thus, an extremely convenient transmit signal can be formed for a receiving apparatus for which demodulation of only some bits (partial bits) of a modulated signal is required.

According to one aspect of a transmitting apparatus of the present invention, a configuration is employed that further includes a coding section that codes transmit bits mapped within the same signal point set together.

According to this configuration, error correction processing can be performed on the receiving side in partial bit units common within a signal point set, enabling partial bits with a significantly lower probability of being erroneous to be obtained on the receiving side with a much simpler configuration.

According to one aspect of a transmitting apparatus of the present invention, the coding section employs a configuration that executes coding with higher error correction capability for transmit bits mapped within the same signal point set than for other transmit bits.

According to this configuration, partial bits with a significantly lower probability of being erroneous can be obtained on the receiving side.

According to one aspect of a receiving apparatus of the present invention, a partial bit demodulation section employs a configuration wherein, in demodulating some bits of a modulated signal that has undergone 64QAM modulation, which bit in a 6-bit bit string making up one symbol is demodulated as a partial bit is changed according to which area on the IQ plane the relevant reception signal point is present in.

According to this configuration, the bit error performance of a partial bit demodulated by the partial bit demodulation section improves, and therefore the reliability of reduced candidate signal points used by the likelihood detection section improves. As a result, the bit error performance of final demodulated bits can be improved.

According to one aspect of a receiving apparatus of the present invention, a configuration is employed that includes: a plurality of QR decomposition sections that perform different QR decomposition; a bit unit branch metric computation section that finds branch metrics for signals obtained by the QR decomposition sections based on rows other than the top row; and a determination section that performs likelihood determination based on those branch metrics.

According to this configuration, computational complexity can be reduced without lowering bit error rate performance when performing MLD using QR decomposition.

The present application is based on Japanese Patent Application No. 2005-153164 filed on May 25, 2005, and Japanese Patent Application No. 2006-70044 filed on Mar. 14, 2006, the entire content of which is expressly incorporated herein by reference.

INDUSTRIAL APPLICABILITY

A receiving apparatus of the present invention can be widely applied to radio communication systems in which different modulated signals are transmitted from a plurality of antennas, such as a MIMO (Multiple-Input Multiple-Output) system or OFDM-MIMO system, for example. 

1. A receiving apparatus that receives a modulated signal transmitted from a transmitting apparatus, said receiving apparatus comprising: a channel fluctuation estimation section that finds a channel estimate of each modulated signal; and a Euclidian distance calculation section that has said channel estimate and said received signal as input, finds a candidate signal point from said channel estimate, and calculates an approximation of a Euclidian distance between said candidate signal point and said received signal using a bit shift and an adder, wherein: said Euclidian distance calculation section: outputs a Euclidian distance approximation as |y| when a size relationship of an I-direction distance x and Q-direction distance y for said candidate signal point and said reception signal point on an IQ plane is |x|<|y| and is also 0<|x|<|y|×(¼+⅛), outputs a Euclidian distance approximation as |y|×(1+⅛) when said size relationship is |x|<|y| and is also|y|×(¼+⅛)<|x|<|y|×(½+⅛), outputs a Euclidian distance approximation as |y|×(1+¼) when said size relationship is |x|<|y| and is also |y|×(½+⅛)<|x|<|y|×(½+¼+⅛), and outputs a Euclidian distance approximation as |y|×(1+¼+⅛) when said size relationship is |x|<|y| and is also |y|×(½+¼+⅛)<|x|.
 2. A receiving apparatus that receives a modulated signal transmitted from a transmitting apparatus, said receiving apparatus comprising: a channel fluctuation estimation section that finds a channel estimate of each modulated signal; and a Euclidian distance calculation section that has said channel estimate and said received signal as input, finds a candidate signal point from said channel estimate, and calculates an approximation of a Euclidian distance between said candidate signal point and said received signal using a bit shift and an adder, wherein: said Euclidian distance calculation section: outputs a Euclidian distance approximation as |x| when a size relationship of an I-direction distance x and Q-direction distance y for said candidate signal point and said reception signal point on an IQ plane is |x|>y| and is also 0<|y|<|x|×(¼+⅛), outputs a Euclidian distance approximation as |x|×(1+⅛)when said size relationship is |x|>|y| and is also |x|×(¼+⅛)<|y|<|x|×(½+⅛), outputs a Euclidian distance approximation as |x|×(1+¼) when said size relationship is |x|>|y| and is also |x|×(½+⅛)<|y|<|x|×(½+¼+⅛), and outputs a Euclidian distance approximation as |x|×(1+¼+⅛) when said size relationship is |x|>|y| and is also |x|×(½+¼+⅛)<|y|.
 3. A receiving apparatus that receives modulated signals transmitted from a transmitting apparatus that transmits different modulated signals from a plurality of antennas, said receiving apparatus comprising: a channel fluctuation estimation section that finds a channel estimate of each modulated signal; a partial bit demodulation section that demodulates only some bits of said modulated signal using a detection method different from likelihood detection; a signal point reduction section that reduces candidate signal points using demodulated partial bits and said channel estimate; and a likelihood detection section that performs likelihood detection using reduced said candidate signal points and a received baseband signal, wherein said likelihood detection section: performs likelihood detection based on a Manhattan distance between said candidate signal point and a reception signal point of said received baseband signal; performs likelihood detection, taking a Euclidian distance approximation to be |y| when a size relationship of an I-direction distance x and Q-direction distance y for said candidate signal point and said reception signal point on an IQ plane is |x|<|y| and is also 0<|x|<|y|×(¼+⅛), taking a Euclidian distance approximation to be |y|×(1+⅛) when said size relationship is |x|<|y| and is also |y|×(¼+⅛)<|x|<|y|×(½+⅛), taking a Euclidian distance approximation to be |y|×(1+¼) when said size relationship is |x|<|y| and is also |y|×(½+⅛)<|x|<|y|×(½+¼+⅛), and taking a Euclidian distance approximation to be |y|×(1+¼+⅛) when said size relationship is |x|<|y| and is also |y|×(½+¼+⅛)<|x|; and performs likelihood detection, taking a Euclidian distance approximation to be |x| when a size relationship of an I-direction distance x and Q-direction distance y for said candidate signal point and said reception signal point on an IQ plane is |x|>|y| and is also 0<|y|<|x|×(¼+⅛), taking a Euclidian distance approximation to be |x|×(1+⅛) when said size relationship is |x|>|y| and is also |x|×(¼+⅛)<|y|<|x|×(½+⅛), taking a Euclidian distance approximation to be |x|×(1+¼) when said size relationship is |x|>|y| and is also |x|×(½+⅛)<|y|<|x|×(½+¼+⅛), and taking a Euclidian distance approximation to be |x|×(1+¼+⅛) when said size relationship is |x|>|y| and is also |x|×(½+¼+⅛)<|y|. 